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  • Coefficient of Determination (R²) | Calculation & Interpretation

Coefficient of Determination (R²) | Calculation & Interpretation

Published on April 22, 2022 by Shaun Turney . Revised on June 22, 2023.

The coefficient of determination is a number between 0 and 1 that measures how well a statistical model predicts an outcome.

Table of contents

What is the coefficient of determination, calculating the coefficient of determination, interpreting the coefficient of determination, reporting the coefficient of determination, practice questions, other interesting articles, frequently asked questions about the coefficient of determination.

The coefficient of determination ( R ²) measures how well a statistical model predicts an outcome. The outcome is represented by the model’s dependent variable .

The lowest possible value of R ² is 0 and the highest possible value is 1. Put simply, the better a model is at making predictions, the closer its R ² will be to 1.

  • If the R 2 is 0, the linear regression model doesn’t allow you to predict exam scores any better than simply estimating that everyone has an average exam score.
  • If the R 2 is between 0 and 1, the model allows you to partially predict exam scores. The model’s estimates are not perfect, but they’re better than simply using the average exam score.
  • If the R 2 is 1, the model allows you to perfectly predict anyone’s exam score.

More technically, R 2 is a measure of goodness of fit. It is the proportion of variance in the dependent variable that is explained by the model.

Graphing your linear regression data usually gives you a good clue as to whether its R 2 is high or low. For example, the graphs below show two sets of simulated data:

  • The observations are shown as dots.
  • The model’s predictions (the line of best fit) are shown as a black line.
  • The distance between the observations and their predicted values (the residuals) are shown as purple lines.

You can see in the first dataset that when the R 2 is high, the observations are close to the model’s predictions . In other words, most points are close to the line of best fit:

Coefficient of determination (R2) = 0.9

In contrast, you can see in the second dataset that when the R 2 is low, the observations are far from the model’s predictions . In other words, when the R 2 is low, many points are far from the line of best fit:

Coefficient of determination (R2) = 0.2

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You can choose between two formulas to calculate the coefficient of determination ( R ²) of a simple linear regression. The first formula is specific to simple linear regressions , and the second formula can be used to calculate the R ² of many types of statistical models.

Formula 1: Using the correlation coefficient

\begin{equation*}R^2=(r)^2\end{equation*}

Where r = Pearson correlation coefficient Example: Calculating R ² using the correlation coefficient You are studying the relationship between heart rate and age in children, and you find that the two variables have a negative Pearson correlation:

\begin{equation*}r=-0.28\end{equation*}

This value can be used to calculate the coefficient of determination ( R ²) using Formula 1:

\begin{equation*}R^2=(-0.28)^2\end{equation*}

Formula 2: Using the regression outputs

\begin{equation*}R^2=1-\dfrac{\textup{RSS}}{\textup{TSS}}\end{equation*}

  • RSS = sum of squared residuals
  • TSS = total sum of squares

\begin{equation*}\textup{RSS}=629.22\end{equation*}

These values can be used to calculate the coefficient of determination ( R ²) using Formula 2:

\begin{equation*}R^2=1-\dfrac{629.22}{2\,187.04}\end{equation*}

You can interpret the coefficient of determination ( R ²) as the proportion of variance in the dependent variable that is predicted by the statistical model .

Another way of thinking of it is that the R ² is the proportion of variance that is shared between the independent and dependent variables.

You can also say that the R ² is the proportion of variance “explained” or “accounted for” by the model. The proportion that remains (1 − R ²) is the variance that is not predicted by the model.

If you prefer, you can write the R ² as a percentage instead of a proportion. Simply multiply the proportion by 100.

R ² as an effect size

Lastly, you can also interpret the R ² as an effect size : a measure of the strength of the relationship between the dependent and independent variables. Psychologist and statistician Jacob Cohen (1988) suggested the following rules of thumb for simple linear regressions :

Be careful: the R ² on its own can’t tell you anything about causation .

  • 71% of the variance in students’ exam scores is predicted by their study time
  • 29% of the variance in student’s exam scores is unexplained by the model
  • The students’ study time has a large effect on their exam scores

Studying longer may or may not cause an improvement in the students’ scores. Although this causal relationship is very plausible, the R ² alone can’t tell us why there’s a relationship between students’ study time and exam scores.

If you decide to include a coefficient of determination ( R ²) in your research paper , dissertation or thesis , you should report it in your results section . You can follow these rules if you want to report statistics in APA Style :

  • You should use “ r ²” for statistical models with one independent variable (such as simple linear regressions). Use “ R ²” for statistical models with multiple independent variables.
  • You don’t need to provide a reference or formula since the coefficient of determination is a commonly used statistic.
  • You should italicize r ² and R ² when reporting their values (but don’t italicize the ²).
  • You shouldn’t include a leading zero (a zero before the decimal point) since the coefficient of determination can’t be greater than one.
  • You should provide two significant digits after the decimal point.
  • Very often, the coefficient of determination is provided alongside related statistical results, such as the F value , degrees of freedom , and p value .

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If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

  • Chi square test of independence
  • Statistical power
  • Descriptive statistics
  • Degrees of freedom
  • Pearson correlation
  • Null hypothesis

Methodology

  • Double-blind study
  • Case-control study
  • Research ethics
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  • Structured interviews

Research bias

  • Hawthorne effect
  • Unconscious bias
  • Recall bias
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  • Self-serving bias
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The coefficient of determination (R²) is a number between 0 and 1 that measures how well a statistical model predicts an outcome. You can interpret the R² as the proportion of variation in the dependent variable that is predicted by the statistical model.

There are two formulas you can use to calculate the coefficient of determination (R²) of a simple linear regression .

R^2=(r)^2

You can use the summary() function to view the R²  of a linear model in R. You will see the “R-squared” near the bottom of the output.

You can use the RSQ() function to calculate R² in Excel. If your dependent variable is in column A and your independent variable is in column B, then click any blank cell and type “RSQ(A:A,B:B)”.

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Relationship Between r and R-squared in Linear Regression

R-squared is a measure of how well a linear regression model fits the data. It can be interpreted as the proportion of variance of the outcome Y explained by the linear regression model.

It is a number between 0 and 1 (0 ≤ R 2 ≤ 1). The closer its value is to 1, the more variability the model explains. And R 2 = 0 means that the model cannot explain any variability in the outcome Y.

On the other hand, the correlation coefficient r is a measure that quantifies the strength of the linear relationship between 2 variables.

r is a number between -1 and 1 (-1 ≤ r ≤ 1):

  • A value of r close to -1 : means that there is negative correlation between the variables (when one increases the other decreases and vice versa)
  • A value of r close to 0 : indicates that the 2 variables are not correlated (no linear relationship exists between them)
  • A value of r close to 1 : indicates a positive linear relationship between the 2 variables (when one increases, the other does)

Here are 3 plots that show the relationship between 2 variables with different correlation coefficients:

  • The left one was drawn with a coefficient r = 0.80
  • The middle one with r = -0.09
  • And the right one with r = -0.76:

plots with different correlation coefficients

Below we will discuss the relationship between r and R 2 in the context of linear regression without diving too deep into the mathematical details.

We start with the special case of a simple linear regression and then discuss the more general case of a multiple linear regression.

R-squared vs r in the case of a simple linear regression

We’ve seen that both r and R-squared measure the strength of the linear relationship between 2 variables, so how do they relate in the case of a simple linear regression?

When we’re dealing with a simple linear regression:

Y = β 0 + β 1 X + ε

R-squared will be the square of the correlation between the independent variable X and the outcome Y :

R 2 = Cor( X , Y) 2

R-squared vs r in the case of multiple linear regression

In simple linear regression we had 1 independent variable X and 1 dependent variable Y, so calculating the the correlation between X and Y was no problem.

In multiple linear regression we have more than 1 independent variable X, therefore we cannot calculate r between more than 1 X and Y.

When dealing with multiple linear regression:

Y = β 0 + β 1 X 1 + β 2 X 2 + β 3 X 3 + β 4 X 4 + … + ε

R-squared will be the square of the correlation between the predicted/fitted values of the linear regression (Ŷ) and the outcome (Y) :

R 2 = Cor( Ŷ , Y) 2

Note that in the special case of the simple linear regression: Cor( X, Ŷ) = 1 So: Cor( X, Y ) = Cor( Ŷ, Y )

Which is why, in that special case: R 2 = Cor( Ŷ, Y ) 2 = Cor( X, Y ) 2

Further reading

  • What is a Good R-Squared Value? [Based on Real-World Data]
  • 7 Tricks to Get Statistically Significant p-Values
  • P-value: A Simple Explanation for Non-Statisticians

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R-squared or coefficient of determination

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  • Interpreting computer regression data
  • Interpreting computer output for regression
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Video transcript

how to interpret r squared values

How to interpret R Squared (simply explained)

R Squared is a common regression machine learning metric, but it can be confusing to know how to interpret the values. In this post, I explain what R Squared is, how to interpret the values and walk through an example.

Stephen Allwright

What is R Squared

R Squared (also known as R2) is a metric for assessing the performance of regression machine learning models. Unlike other metrics, such as MAE or RMSE , it is not a measure of how accurate the predictions are, but instead a measure of fit. R Squared measures how much of the dependent variable variation is explained by the independent variables in the model.

R Squared mathematical formula

The formula for calculating R Squared is as follows:

r squared mathematical formula

How to interpret R Squared

R Squared can be interpreted as the percentage of the dependent variable variance which is explained by the independent variables. Put simply, it measures the extent to which the model features can be used to explain the model target.

For example, an R Squared value of 0.9 would imply that 90% of the target variance can be explained by the model features, whilst a value of 0.2 would suggest that the model features are only able to account for 20% of the variance.

R Squared valued interpretation

Now that we understand how to interpret the meaning of R Squared , let’s look at how to interpret the different values that it can produce. This will be dependent upon your use case and dataset, but a general rule that I follow is:

R Squared interpretation example

Let’s use our understanding from the previous sections to walk through an example. I will be calculating the R Squared value and subsequent interpretation for an example where we want to understand how much of the Height variance can be explained by Shoe Size.

The R Squared value for these predictions is:

R Squared = 0.88

The interpretation of this value is:

88% of the variance in Height is explained by Shoe Size, which is commonly seen as a significant amount of the variance being explained.

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I'm a Data Scientist currently working for Oda, an online grocery retailer, in Oslo, Norway. These posts are my way of sharing some of the tips and tricks I've picked up along the way.

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What Is R-Squared?

Formula for r-squared, what r-squared can tell you, r-squared vs. adjusted r-squared, r-squared vs. beta, limitations of r-squared, the bottom line.

  • Corporate Finance
  • Financial Analysis

R-Squared: Definition, Calculation Formula, Uses, and Limitations

report r or r2

Yarilet Perez is an experienced multimedia journalist and fact-checker with a Master of Science in Journalism. She has worked in multiple cities covering breaking news, politics, education, and more. Her expertise is in personal finance and investing, and real estate.

report r or r2

R-squared (R 2 ) is a statistical measure that represents the proportion of the variance for a dependent variable that’s explained by an independent variable in a regression model.

Whereas correlation explains the strength of the relationship between an independent and a dependent variable, R-squared explains the extent to which the variance of one variable explains the variance of the second variable. So, if the R 2  of a model is 0.50, then approximately half of the observed variation can be explained by the model’s inputs.

Key Takeaways

  • R-squared is a statistical measure that indicates how much of the variation of a dependent variable is explained by an independent variable in a regression model.
  • In investing, R-squared is generally interpreted as the percentage of a fund’s or security’s price movements that can be explained by movements in a benchmark index.
  • An R-squared of 100% means that all movements of a security (or other dependent variable) are completely explained by movements in the index (or whatever independent variable you are interested in).

Xiaojie Liu / Investopedia

R 2 = 1 − Unexplained Variation Total Variation \begin{aligned} &\text{R}^2 = 1 - \frac{ \text{Unexplained Variation} }{ \text{Total Variation} } \\ \end{aligned} ​ R 2 = 1 − Total Variation Unexplained Variation ​ ​

The calculation of R-squared requires several steps. This includes taking the data points (observations) of dependent and independent variables and finding the line of best fit , often from a regression model. From there, you would calculate predicted values, subtract actual values, and square the results. This yields a list of errors squared, which is then summed and equals the unexplained variance.

To calculate the total variance, you would subtract the average actual value from each of the actual values, square the results, and sum them. From there, divide the first sum of errors (unexplained variance) by the second sum (total variance), subtract the result from one, and you have the R-squared. 

In investing , R-squared is generally interpreted as the percentage of a fund’s or security’s movements that can be explained by movements in a benchmark index. For example, an R-squared for a fixed-income security vs. a bond index identifies the security’s proportion of price movement that is predictable based on a price movement of the index.

The same can be applied to a stock vs. the S&P 500 Index or any other relevant index. It may also be known as the co-efficient of determination .

R-squared values range from 0 to 1 and are commonly stated as percentages from 0% to 100%. An R-squared of 100% means that all of the movements of a security (or another dependent variable) are completely explained by movements in the index (or whatever independent variable you are interested in).

In investing, a high R-squared, from 85% to 100%, indicates that the stock’s or fund’s performance moves relatively in line with the index. A fund with a low R-squared, at 70% or less, indicates that the fund does not generally follow the movements of the index. A higher R-squared value will indicate a more useful beta figure. For example, if a stock or fund has an R-squared value of close to 100%, but has a beta below 1, it is most likely offering higher risk-adjusted returns .

R-squared only works as intended in a simple linear regression model with one explanatory variable. With a multiple regression made up of several independent variables, the R-squared must be adjusted.

The adjusted R-squared compares the descriptive power of regression models that include diverse numbers of predictors. Every predictor added to a model increases R-squared and never decreases it. Thus, a model with more terms may seem to have a better fit just for the fact that it has more terms, while the adjusted R-squared compensates for the addition of variables; it only increases if the new term enhances the model above what would be obtained by probability and decreases when a predictor enhances the model less than what is predicted by chance.

In an  overfitting  condition, an incorrectly high value of R-squared is obtained, even when the model actually has a decreased ability to predict. This is not the case with the adjusted R-squared.

Beta and R-squared are two related, but different, measures of correlation . Beta is a measure of relative riskiness. A mutual fund with a high R-squared correlates highly with a  benchmark . If the beta is also high, it may produce higher returns than the benchmark, particularly in  bull markets .

R-squared measures how closely each change in the price of an asset is correlated to a benchmark. Beta measures how large those price changes are relative to a benchmark. Used together, R-squared and beta can give investors a thorough picture of the performance of asset managers. A beta of exactly 1.0 means that the risk (volatility) of the asset is identical to that of its benchmark.

Essentially, R-squared is a statistical analysis technique for the practical use and trustworthiness of betas of securities.

R-squared will give you an estimate of the relationship between movements of a dependent variable based on an independent variable’s movements. However, it doesn’t tell you whether your chosen model is good or bad, nor will it tell you whether the data and predictions are biased.

A high or low R-squared isn’t necessarily good or bad—it doesn’t convey the reliability of the model or whether you’ve chosen the right regression. You can get a low R-squared for a good model, or a high R-squared for a poorly fitted model, and vice versa.

What is a ‘good’ R-squared value?

What qualifies as a “good” R-squared value will depend on the context. In some fields, such as the social sciences, even a relatively low R-squared value, such as 0.5, could be considered relatively strong. In other fields, the standards for a good R-squared reading can be much higher, such as 0.9 or above. In finance, an R-squared above 0.7 would generally be seen as showing a high level of correlation, whereas a measure below 0.4 would show a low correlation. This is not a hard rule, however, and will depend on the specific analysis.

What does an R-squared value of 0.9 mean?

Essentially, an R-squared value of 0.9 would indicate that 90% of the variance of the dependent variable being studied is explained by the variance of the independent variable. For instance, if a mutual fund has an R-squared value of 0.9 relative to its benchmark, this would indicate that 90% of the variance of the fund is explained by the variance of its benchmark index.

Is a higher R-squared better?

Here again, it depends on the context. Suppose you are searching for an index fund that will track a specific index as closely as possible. In that scenario, you would want the fund’s R-squared value to be as high as possible since its goal is to match—rather than trail—the index. On the other hand, if you are looking for actively managed funds, then a high R-squared value might be seen as a bad sign, indicating that the funds’ managers are not adding sufficient value relative to their benchmarks.

R-squared can be useful in investing and other contexts, where you are trying to determine the extent to which one or more independent variables affect a dependent variable. However, it has limitations that make it less than perfectly predictive.

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Statistics Made Easy

How to Interpret Adjusted R-Squared (With Examples)

When we fit linear regression models we often calculate the R-squared value of the model.

The R-squared value is the proportion of the variance in the response variable that can be explained by the predictor variables in the model.

The value for R-squared can range from 0 to 1 where:

  • A value of 0 indicates that the response variable cannot be explained by the predictor variables at all.
  • A value of 1 indicates that the response variable can be perfectly explained by the predictor variables.

Although this metric is commonly used to assess how well a regression model fits a dataset, it has one serious drawback:

The drawback of R-squared:   R-squared will always increase when a new predictor variable is added to the regression model.

Even if a new predictor variable is almost completely unrelated to the response variable, the R-squared value of the model will increase, if only by a small amount.

For this reason, it’s possible that a regression model with a large number of predictor variables has a high R-squared value, even if the model doesn’t fit the data well.

Fortunately there is an alternative to R-squared known as adjusted R-squared .

The adjusted R-squared is a modified version of R-squared that adjusts for the number of predictors in a regression model.

It is calculated as:

Adjusted R 2 = 1 – [(1-R 2 )*(n-1)/(n-k-1)]

  • R 2 : The R 2 of the model
  • n : The number of observations
  • k : The number of predictor variables

Because R-squared always increases as you add more predictors to a model, the adjusted R-squared can tell you how useful a model is, adjusted for the number of predictors in a model .

The advantage of Adjusted R-squared:   Adjusted R-squared tells us how well a set of predictor variables is able to explain the variation in the response variable, adjusted for the number of predictors in a model .   Because of the way it’s calculated, adjusted R-squared can be used to compare the fit of regression models with different numbers of predictor variables.

To gain a better understanding of adjusted R-squared, check out the following example.

Example: Understanding Adjusted R-Squared in Regression Models

Suppose a professor collects data on students in his class and fits the following regression model to understand how hours spent studying and current grade in the class affect the score a student receives on the final exam.

Exam Score = β 0 + β 1 (hours spent studying) + β 2 (current grade)

Suppose this regression model has the following metrics:

  • R-squared: 0.955
  • Adjusted R-squared: 0.946

Now suppose the professor decides to collect data on another variable for each student: shoe size.

Although this variable should be completely unrelated to the final exam score, he decides to fit the following regression model:

Exam Score = β 0 + β 1 (hours spent studying) + β 2 (current grade) + β 3 (shoe size)

  • R-squared: 0.965
  • Adjusted R-squared: 0.902

If we only looked at the R-squared values for each of these two regression models, we would conclude that the second model is better to use because it has a higher R-squared value!

However, if we look at the adjusted R-squared values then we come to a different conclusion: The first model is better to use because it has a higher adjusted R-squared value.

The second model only has a higher R-squared value because it has more predictor variables than the first model.

However, the predictor variable that we added (shoe size) was a poor predictor of final exam score, so the adjusted R-squared value penalized the model for adding this predictor variable.

This example illustrates why adjusted R-squared is a better metric to use when comparing the fit of regression models with different numbers of predictor variables.

Additional Resources

The following tutorials explain how to calculated adjusted R-squared values using different statistical software:

How to Calculate Adjusted R-Squared in R How to Calculate Adjusted R-Squared in Excel How to Calculate Adjusted R-Squared in Python

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Reporting of R 2 Statistics for Mixed-Effects Regression Models

  • 1 Department of Neurology, Johns Hopkins University School of Medicine, Baltimore, Maryland
  • 2 Department of Biostatistics, Johns Hopkins University, Baltimore, Maryland
  • Original Investigation Assessing Biological and Methodological Aspects of Brain Volume Loss in Multiple Sclerosis Magí Andorra, MSc; Kunio Nakamura, PhD; Erika J. Lampert, BSc; Irene Pulido-Valdeolivas, MD, PhD; Irati Zubizarreta, MD; Sara Llufriu, MD, PhD; Eloy Martinez-Heras, PhD; Nuria Sola-Valls, MD; María Sepulveda, MD; Ana Tercero-Uribe, MD; Yolanda Blanco, MD, PhD; Albert Saiz, MD, PhD; Pablo Villoslada, MD, PhD; Elena H. Martinez-Lapiscina, MD, PhD JAMA Neurology
  • Comment & Response Reporting of R 2 Statistics for Mixed-Effects Regression Models—Reply Magi Andorra, MSc; Elena H. Martinez-Lapiscina, MD, PhD JAMA Neurology

To the Editor We read with interest the article by Andorra et al 1 that evaluated the dynamics of brain volume loss in multiple sclerosis and modeled these variables in mixed-effects regression models as functions of disease duration. The authors report various goodness-of-fit measures of their models, focusing on the coefficient of determination ( R 2 ), which ranges from 0 to 1 and represents the proportion of variance in the dependent variable explained by the model. For a model such as ordinary least squares regression, which includes only fixed-effects components, the interpretation of the R 2 is intuitive and represents the variance of the dependent variable explained by the independent variable(s). For mixed-effects regression models, there are several variance components, which include both fixed and random effects. Andorra et al 1 cite methods developed by Nakagawa and Schielzeth 2 in calculating their article’s R 2 values. The methods of Nakagawa and Schielzeth define R 2 statistics for mixed-effects models as follows: (1) marginal R 2 (variance explained by only fixed effects) and (2) conditional R 2 (variance explained by both fixed and random effects). The marginal R 2 is consistent with how most readers will interpret an R 2 statistic (using the traditional ordinary least squares interpretation). Notably, Nakagawa and Schielzeth recommend that both marginal and conditional R 2 be reported given that they convey unique and distinctive information.

Sotirchos ES , Fitzgerald KC , Crainiceanu CM. Reporting of R 2 Statistics for Mixed-Effects Regression Models. JAMA Neurol. 2019;76(4):507. doi:10.1001/jamaneurol.2018.4720

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“From R to your manuscript”

report ’s primary goal is to bridge the gap between R’s output and the formatted results contained in your manuscript. It automatically produces reports of models and data frames according to best practices guidelines (e.g., APA ’s style), ensuring standardization and quality in results reporting.

Installation

The package is available on CRAN and can be downloaded by running:

If you would instead like to experiment with the development version, you can download it from GitHub :

Load the package every time you start R

Tip Instead of library(report) , use library(easystats) . This will make all features of the easystats-ecosystem available. To stay updated, use easystats::install_latest() .

Documentation

The package documentation can be found here .

Report all the things

General workflow.

The report package works in a two step fashion. First, you create a report object with the report() function. Then, this report object can be displayed either textually (the default output) or as a table, using as.data.frame() . Moreover, you can also access a more digest and compact version of the report using summary() on the report object.

The report() function works on a variety of models, as well as other objects such as dataframes:

These reports nicely work within the tidyverse workflow:

t -tests and correlations

Reports can be used to automatically format tests like t -tests or correlations.

As mentioned, you can also create tables with the as.data.frame() functions, like for example with this correlation test:

This works great with ANOVAs, as it includes effect sizes and their interpretation.

Generalized Linear Models (GLMs)

Reports are also compatible with GLMs, such as this logistic regression :

Mixed Models

Mixed models, whose popularity and usage is exploding, can also be reported:

Bayesian Models

Bayesian models can also be reported using the new SEXIT framework, which combines clarity, precision and usefulness.

Other types of reports

Specific parts.

One can, for complex reports, directly access the pieces of the reports:

Report participants’ details

This can be useful to complete the Participants paragraph of your manuscript.

Report sample

Report can also help you create a sample description table (also referred to as Table 1 ).

Report system and packages

Finally, report includes some functions to help you write the data analysis paragraph about the tools used.

If you like it, you can put a star on this repo, and cite the package as follows:

report is a young package in need of affection . You can easily be a part of the developing community of this open-source software and improve science! Don’t be shy, try to code and submit a pull request (See the contributing guide ). Even if it’s not perfect, we will help you make it great!

Code of Conduct

Please note that the report project is released with a Contributor Code of Conduct . By contributing to this project, you agree to abide by its terms.

Monthly Downloads

Last published, functions in report (0.5.8).

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President Joseph R. Biden, Jr. spoke today with President Xi Jinping of the People’s Republic of China (PRC).  The call follows the two leaders’ meeting in Woodside, California in November 2023.  The two leaders held a candid and constructive discussion on a range of bilateral, regional, and global issues, including areas of cooperation and areas of difference.  They reviewed and encouraged progress on key issues discussed at the Woodside Summit, including counternarcotics cooperation, ongoing military-to-military communication, talks to address AI-related risks, and continuing efforts on climate change and people-to-people exchanges.   President Biden emphasized the importance of maintaining peace and stability across the Taiwan Strait and the rule of law and freedom of navigation in the South China Sea.  He raised concerns over the PRC’s support for Russia’s defense industrial base and its impact on European and transatlantic security, and he emphasized the United States’ enduring commitment to the complete denuclearization of the Korean Peninsula.  President Biden also raised continued concerns about the PRC’s unfair trade policies and non-market economic practices, which harm American workers and families.  The President emphasized that the United States will continue to take necessary actions to prevent advanced U.S. technologies from being used to undermine our national security, without unduly limiting trade and investment. The two leaders welcomed ongoing efforts to maintain open channels of communication and responsibly manage the relationship through high-level diplomacy and working-level consultations in the weeks and months ahead, including during upcoming visits by Secretary Yellen and Secretary Blinken.

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Alienware m18 R2 review: A premium, beastly laptop for no-compromises gaming

Last year's Alienware m18 was already good, but the m18 R2 and its 14th-gen HX processor and RTX 4090 graphics is excellent.

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Pricing and availability, design and ports, keyboard and touchpad, performance, should you buy the alienware m18 r2.

Dell announced a new lineup of gaming laptops earlier this year at CES 2024, including the Alienware m18 R2. It's a gaming powerhouse with an 18-inch display that succeeds the original Alienware m18 R1. Unlike its smaller counterpart, the m16 R2, Dell didn't redesign the Alienware m18 R2 this year. Instead, the m18 R2 got a spec bump. The laptop still features Nvidia GeForce RTX 40-series graphics, but now includes the Intel 14th-generation HX processor platform. While not as flashy of an upgrade, this makes the m18 R2 — which was already an excellent performer — even better. It'll easily replace the outgoing Alienware m18 R1 as our favorite 18-inch laptop for gaming.

Usually, picking out a gaming laptop means giving up a few things based on your needs. You can pick a laptop with a great display and a thin form factor, but you'll give up performance. However, the Alienware m18 R2 puts together all the essential features of a quality gaming PC and crams them into a tiny form factor. It has a responsive and color-accurate display, fast gaming performance, and a compact design. There are two main compromises that you'll make by choosing the m18 R2, and those are the laptop's weight and price. If you can deal with a heavy laptop and are willing to pay a lot, the Alienware m18 R2 won't disappoint.

About this review: Dell loaned us an Alienware m18 R2 for review. The company had no input in this review, and did not see its contents before publishing.

report r or r2

Alienware m18 R2

It'll crush any game and provide stunning graphics

Dell took the Alienware m18 and gave it a boost to Intel's 14th-generation HX platform for the R2 model, and made an already-good gaming laptop great. Owners of the original Alienware m18 or another Nvidia RTX 40-series laptop probably won't feel the need to upgrade. However, people looking for a no-compromises gaming laptop will love the m18 R2. It crushes in-game performance, has a stunning display, and features a sleek design.

  • Having 14th-gen HX Intel processors and Nvidia RTX 40-series GPUs makes for a performance champion
  • The display is excellent and responsive, with great color accuracy
  • The design and build is better than similarly-priced gaming laptops
  • Superb port selection includes Thunderbolt 4, SD, and more
  • Some m18 R2 configurations can weigh nearly 10 pounds
  • The laptop is fairly thin, but it's still not very portable
  • The speakers lack fullness, sound tinny, and could be better overall
  • Our review unit as tested is expensive, retailing for $3,600

The Alienware m18 R2 released earlier this year as a follow-up to the original Alienware m18, which was a performance-focused gaming laptop. There is a lot of variety in the Alienware m18 R2's price and performance, depending on the configuration you choose. The laptop starts at $1,900, and includes an Intel Core i7 processor, Nvidia RTX 4060 graphics, and a 1200p display. As tested, our review unit retails for $3,600 and includes the top-of-the-line Intel Core i9 processor, Nvidia RTX 4090 GPU, and 1600p display. Keep in mind when configuring your m18 R2 that cheaper configurations will undoubtedly perform worse than the expensive configuration we reviewed.

Alienware m18

Sleek, heavy, and packed with a ton of connectivity options.

The Alienware m18 R2 is one of the better-looking gaming laptops out there, featuring a thin form factor and a chassis made of mostly metal. At its thickest point, the laptop is just over an inch thick. The design is subtle, and if not for the large thermal shelf, you might mistake it for a large workstation laptop. There are some RGB elements, such as the Alienware logo and the loop around the back of the thermal shelf. However, compared to most gaming laptops, the design of the Alienware m18 R2 offers a low-key look.

The Alienware m18 R2 is one of the better-looking gaming laptops out there, featuring a thin form factor and a chassis made of mostly metal.

Dell redesigned the Alienware m16 R2 this year, ditching the laptop's thermal shelf to make it more portable and better looking. But the bigger Alienware m18 R2 retains this element in order to keep its high-end components and larger cooling system. The m18 R2 is also extremely heavy, with the heaviest configuration weighing nearly 10 pounds.

The Alienware m18 R2 offers plenty of ports, and they're spread out between the back and sides of the laptop. On the right side of the m18 R2, there's a USB-C port near the palm rest that is extremely easy to access in a pinch. The back houses most of the I/O options, including two Thunderbolt 4 ports, a USB-A port, an HDMI port, a mini-DisplayPort, an SD card reader, and a barrel charging port. The left side offers two more USB-A ports, an RJ45 jack, and a 3.5mm audio jack. Put simply, the m18 R2 will be able to handle all of your connectivity needs.

Alienware m16 R2 review: A seismic shift in direction

The cherry mx mechanical laptop switches are a game-changer.

There are a few benefits that you'll receive from picking a big, bulky 18-inch laptop over something smaller. The obvious thing is performance, but on the Alienware m18 R2, a more subtle one is the keyboard and touchpad. The m18 R2 features fully-mechanical switches with 1.8mm of total travel, and that made it the best laptop keyboard I've ever used. The switches are CherryMX variants modified to fit in the laptop form factor, and they are excellent. You can feel and hear the click of each key, which feels the same regardless of where you press it. Underneath, the keyboard offers per-key RGB lighting that can be customized in software.

The m18 R2 features fully-mechanical switches with 1.8mm of total travel, and that made it the best laptop keyboard I've ever used.

There is also a numpad and plenty of function keys, as well as full-sized arrow keys. The arrow keys aren't shifted down on the m18 R2 like some other gaming laptops, but that wasn't an issue while gaming. Of the standard function keys, there are a few specifically designed for the m18 R2. The F1 key, for example, changes the laptop's performance mode. The F2 key can activate "stealth mode," a setting that will tame the fans and RGB elements to make the laptop blend in better.

Cherry MX2A keyboard switch review: Is this the next phase for switches?

As for the touchpad, it's good for a gaming laptop, but you'll still want to use a mouse whenever possible. The area of the touchpad isn't as large as you might expect, considering the 18-inch form factor. However, the thermal shelf and cooling system in the Alienware m18 R2 pushes the keyboard down. This limits how much diagonal space can be allocated to a large touchpad.

The CherryMX keyboard is an optional add-on for the m18 R2, so make sure you select it at checkout if you want it. Otherwise, you'll get the standard Alienware M Series keyboard.

Visually stunning in everyday use, and color-accurate in display tests

The Alienware m18 R2 comes with a lot of configuration options for many of its components, and the display is no different. With the screen, you have to decide whether you prioritize refresh rate or resolution. One option is an 18-inch, QHD+ display with a 2560 x 1600 resolution and a 165Hz refresh rate. The other is an 18-inch, FHD+ panel with a 1920 x 1200 resolution and a 480Hz refresh rate. The 480Hz refresh rate option will certainly feel more responsive than the 166Hz variant, the latter of which I tested. There are some similarities between the two panels, such as Dell's claimed 100% coverage of the DCI-P3 color gamut.

Before even running my display tests, I noticed the colors popped more than usual in Forza Horizon 5 . Gaming laptops aren't often known for their color accuracy, so the difference between the Alienware m18 R2 and other laptops I've tested recently was immediately perceptible. The display blows the ones on cheaper gaming laptops, like the Lenovo LOQ 15, out of the water. The tests back this up, too. I measured 100% coverage of the sRGB gamut, and 99% coverage of the DCI-P3 gamut. The last number is slightly less than Dell claims, but my result is definitely within the margin of error for my testing equipment.

Before even running my display tests, I noticed the colors popped more than usual in Forza Horizon 5 .

Lenovo LOQ 15 (15IAX9I) review: It feels like a $750 gaming laptop, but performs better

For my needs, I'd rather have the higher resolution display on the m18 R2 than the higher refresh rate. The 165Hz screen was more than enough for games to feel snappy and smooth in my testing. However, if you're a professional gamer playing at a high level, you might be able to get more usage out of the better responsiveness. Speaking of, both versions of the display feature 3ms gray-to-gray response time. Regardless of which one you choose, the colors will be vibrant and stunning. Dell advertises a 300-nit brightness rating, and my unit actually beat that in our tests, measuring 313 nits.

I hate to sound cliché, but this laptop handles everything you throw at it

Even on gaming laptops with RTX 40-series graphics cards, I often have to turn down the graphics settings on my favorite games to get high refresh rates. However, with the Intel Core i9 14900 HX processor and RTX 4090 graphics card, the Alienware m18 R2 was different. Every game I tried on the m18 R2 ran on the highest settings by default after detecting my system's components. I manually adjusted a few things to make sure I was stressing the Alienware m18 R2 as much as possible, and the laptop still didn't show many signs of faltering. The computer did begin to get hot, and the fans became loud, but that was to be expected.

I manually adjusted a few things to make sure I was stressing the Alienware m18 R2 as much as possible, and the laptop still didn't show many signs of faltering.

I played a variety of titles on the Alienware m18 R2, including Fortnite , Forza Horizon 5 , and Grand Theft Auto V . Fortnite ran at the highest "epic" settings and unlimited frame rates with no problems at all, and the game hovered around 80–120 FPS most of the time. In Forza Horizon 5 , the m18 R2 put up a score of 82 FPS while running on the "extreme" preset. There wasn't a single game I tried that didn't run at the highest setting at frame rates well above playable levels.

You can see how the Alienware m18 R2 performs against other high-end RTX 4090 systems, as well as the smaller m16 R2 with the RTX 4070, in the table below. We tested the laptop in PCMark 10, Geekbench 6, 3DMark: Time Spy Extreme, and Cinebench 2024 using the "performance" mode while connected to power.

As the results show, the Alienware m18 R2 can hang with the best of the best in terms of performance. The laptop beat the liquid-cooled Lenovo Legion 9i in PCMark 10 thanks to its 14th-gen HX processor, but narrowly lost to the Legion 9i in graphics-based tests. Compared to the Asus ROG Strix Scar 16 , which has the same CPU and GPU as the Alienware m18 R2, the m18 R2 lagged behind slightly in most tests. However, the m18 R2 did manage to beat out the Strix Scar 16 in the Cinebench 2024 graphics test. Keep in mind that you will see a performance dropoff on battery power, but the m18 R2 will remain a great performer. I expect most people to use the m18 R2 connected to wall power often, but when using battery, you'll get anywhere from a few hours to five or six depending on the performance setting and your tasks.

Lenovo Legion 9i review: The best gaming laptop money can buy

You should buy the Alienware m18 R2 if:

  • You want an expensive, large laptop for no-compromise gaming
  • You want the latest Intel processor and Nvidia graphics card for gaming
  • You're willing to pay a lot for an all-in-one laptop gaming setup

You should NOT buy the Alienware m18 R2 if:

  • You want a portable gaming laptop for travel, or a dual-purpose laptop for work and play
  • You would do fine with a cheaper laptop with decent specs and a more approachable price
  • You'd rather buy a gaming laptop that is larger and bulkier, but lighter

An 18-inch gaming laptop like the Alienware m18 R2 appeals to a niche audience. That's because laptops with the size and weight of the m18 R2 are certainly not portable, and they can be very expensive as well. For these reasons, the Alienware m18 R2 makes sense for someone who wants to play PC games without the hassle of building a gaming PC. Going a step further, laptops like the m18 R2 are for people who don't even want to build a setup around a great pre-built gaming PC . The Alienware m18 R2 is an all-in-one package with a great display, refined design, and top-of-the-line components for excellent performance. If you're willing to pay the price required to check all those boxes in the laptop form factor, you'll enjoy the Alienware m18 R2.

Want a large gaming laptop that'll become an all-in-one gaming powerhouse? With a 14th-generation HX processor and Nvidia RTX 40-series graphics, the Alienware m18 R2 is up for the challenge. You'll just have to look past the heavy build and high price tag for higher-end configurations.

Business | Rivian hosts R2 open house in Normal, its new…

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Business | Rivian hosts R2 open house in Normal, its new production home

Kyle Matas, center, shows the interior of Rivian’s R3 model to his children, Able Matas, left, and Quinn Matas, during an unveiling of new Rivians on April 6, 2024, in Normal. (Trent Sprague/for the Chicago Tribune)

NORMAL — Nearly five years after unveiling its prototype electric pickup truck and SUV for a Normal community looking to restart its idled auto plant, Rivian was back in the town circle Saturday with its second-generation EVs, and the promise of more activity at the now-bustling factory.

The low-key but festive event showcased the midsize R2 SUV, which will be built in Normal after Rivian delayed plans for a second plant in Georgia. The smaller and sportier R3 crossover, whose production plans have yet to be announced, was also on display.

Rivian revealed both new models last month, while announcing that the R2, at least initially, will be made in Illinois . The company received more than 68,000 preorders for the $45,000 R2 within 24 hours of its online debut.

“It not only allows us to save a lot of capital, it allows us to launch the vehicle sooner,” said Rivian CEO and founder R.J. Scaringe at Saturday’s event. “And based on the reaction to the product, it’s important we launch this as quickly as possible.”

Hundreds of people arrived Saturday on a cool but sunny spring morning, where proptypes of the R2, R3 and R3X were swarmed by a tire-kicking, photo-snapping crowd of EV enthusiasts and Rivian boosters, of which there are many in Normal.

Rivian builds its inaugural full-size electric R1T pickup truck, R1S SUV and commercial delivery vans for Amazon and AT&T in a renovated 4 million-square-foot auto plant on the outskirts of the college town about 130 miles south of Chicago.

The plant employs 7,000 assembly workers, up from zero after Mitsubishi closed the factory nearly a decade ago.

Scaringe purchased the shuttered factory for $16 million from a liquidation firm in January 2017. Boosted by more than $1 billion in investment and expansion, the plant has built more than 100,000 EVs since restarting production in 2021.

Rivian is expected to save more than $2.25 billion in capital expense by launching production of the R2 alongside the rest of its lineup in Normal and putting plans to build the $5 billion Georgia plant on hold, Scaringe said.

An employee checks details on the Rivian R3X model prior to an unveiling of new models on April 6, 2024, in Normal. (Trent Sprague/for the Chicago Tribune)

“There’s also advantages just in terms of having the teams and the processes and the systems that are now really starting to work well in our Normal facility and leveraging those to launch R2,” said Scaringe.

Rivian built nearly 14,000 EVs in the first quarter and is on target to produce 57,000 vehicles in Normal this year. None of them will be built over the next three weeks, however.

The plant is shutting down for retooling Monday to streamline operations. When it reopens April 28, it will go from three shifts to two, with all assembly line workers expected to keep their jobs, albeit on different schedules.

“We are increasing the overall capacity and efficiency of our lines,” said Tim Fallon, 44, a former Nissan executive who has been vice president of manufacturing operations at the Normal plant since 2022. “Plus, we’re also making a lot of upgrades to our vehicles, many that you won’t see, but they help us with our costs.”

Fallon said the plant will come out of the shutdown operating at a higher line rate, which will enable it to still hit production targets for the year. The first major retooling since restarting the plant is not directly related to the future production of the R2, he said.

The R2 event comes as the rate of EV growth is beginning to slow, hindered by consumer concern about everything from range anxiety and charging infrastructure to sticker shock.

The Rivian R2 during an unveiling of new Rivians in Normal on April 6, 2024. (Trent Sprague/for the Chicago Tribune)

EV market share is expected to reach 8% of total new vehicle sales in 2024, up from 6.9% last year, according to the car shopping website Edmunds. EVs topped the 1 million sales mark in the U.S. last year for the first time.

Through February, EV sales totaled about 161,000 units, or 6.9% of the U.S. new car market, Edmunds said. That’s up 15% from the 140,000 EVs sold during the first two months last year, but far below the 64% growth rate over January – February 2022.

The slowing pace of EV adoption has caused a number of automakers — including Rivian — to adjust their course.

Last week, market leader Tesla announced an 8.5% decline in EVs delivered in the first quarter and reportedly has abandoned plans to build a lower-priced Model 2 for the masses. Meanwhile, Ford said Thursday it would delay rolling out a new electric pickup and SUV until 2026 and 2027, respectively, as it adds gas-electric hybrids to its lineup, a growing trend in the industry.

In February, California-based Rivian laid off 10% of its salaried workforce , including a small number of employees at its Normal assembly plant, amid the broader slowdown.

Rivian generated $1.3 billion in revenue and lost more than $1.5 billion in the fourth quarter of 2023. The company had $7.86 billion in cash as of Dec. 31.

But at $45,000 for the R2, Rivian may be in the sweet spot for demand. A study last month by Edmunds found that 47% of potential EV buyers are seeking to spend less than $40,000, while 42% want an SUV or crossover.

Last year, the average transaction price of an electric vehicle was $61,702, while all other vehicles stood at $47,450, Edmunds said. Rivian’s R1 models start at about $70,000.

“The R2 being at $45,000 is something that the vast majority of the population can look at as an option,” Scaringe said. “There’s a lack of choice, we believe, in that price category for really nicely done EVs.”

More than 3,000 people pre-registered for the four-hour event Saturday, showing up at scheduled half-hour intervals to afford an unhurried look at the new models.

Many circled around the R2, R3 and R3X prototypes in the open-air showroom, comparing notes, taking photos and in some cases, plunking down a $100 refundable deposit to reserve the first ones off the line in about two years.

Kyle Conner, 28, an EV YouTube content creator, drove 1,000 miles from his Fort Collins, Colorado, home in a Tesla to get an up close look and post videos of the new Rivian models in Normal. Conner, who also owns a Rivian R1, said the R2 will likely be a big hit, despite a few reservations.

Among the many features that caught his eye, the R2 is the first Rivian built with a native port for the Tesla Supercharger network.

Last year, Tesla agreed to make its highly-rated charging network accessible to Rivian and other manufacturers, enabling it to tap into $7.5 billion of federal funding from President Joe Biden’s bipartisan infrastructure law to expand public EV charging capacity.

Conner said the biggest selling point for the R2 was the $45,000 price tag. “What we don’t know yet are the final specifications,” he said.

Cassy Taylor, 55, of Lexington, who serves as the McLean County administrator, was considering putting the $100 deposit on the R2 Saturday after seeing it in person.

Taylor, who drives a Subaru Crosstrek, has been eyeing a Rivian since it launched production two-and-a-half years ago. She said the R2 is a better size for her than the R1.

“They’re smaller vehicles, similar to the SUV I drive now,” Taylor said. “I think that might be more suitable for my needs and easier to park.”

Knowing that it will be built in Normal may have sealed the deal for her.

“It’s an investment in our community,” Taylor said. “And we’re really excited that they are making the cars here.”

Matt McLoughlin, 38, of Mackinaw, a test technician at Rivian since 2021, came to the event Saturday for his first look at the new models. Set to go on break during the factory retooling, he used his first day off to get a glimpse of the future.

“I am totally excited for the opportunity to build the R2 in Normal,” McLoughlin said. “It is a huge opportunity for us.”

Rivian was initially lured to Illinois by $4 million in local incentives and about $50 million in state tax credits over 15 years if it meets employment and investment targets at the Normal facility. Those goals included creating 1,000 jobs by 2024, a number it has long since surpassed.

In addition to expediting production, Rivian may have had another motive for doubling down on Illinois — new financial incentives dangled by the state.

“DCEO has been in conversations with Rivian about potential incentives for its planned expansion,” said Eliza Glezer, a spokesperson for the Illinois Department of Commerce & Economic Opportunity. “No incentives have been executed for the R2 expansion.”

While the shift of initial R2 production to Normal may be a near-term boon for the central Illinois plant, one prominent auto industry analyst predicted Rivian’s long-term manufacturing future remained in Georgia.

Sam Fiorani, vice president of global vehicle forecasting at AutoForecast Solutions, a market research firm, said Rivian may move production of the R1, R2 and R3 to the planned Georgia plant by the end of the decade, seeking improved efficiency, volume and a larger pool of assembly workers.

In such a case, the Normal plant may either be reduced to the narrower and more competitive lane of commercial EV production, or close entirely, he said.

“If the company is doing well, the likelihood of them building the second plant and moving there is high,” Fiorani said.

The Georgia plant likely won’t open until 2027, and its future may depend on the initial success of Rivian to ramp up production and sales of its next-generation R2 out of the Normal plant, Fiorani said.

“If they don’t start making money, and soon, the idea of moving to Georgia could be put on the back burner even further,” Fiorani said.

On Saturday, Scaringe dismissed that theory, reiterating his commitment to Georgia and Normal, which he said would be the production home to the R1 for the foreseeable future.

He also hinted that R2 and potentially R3 — which is built on the same platform — could be made in Illinois, even after Georgia opens.

“Normal will do R1, R2 and potentially more,” Scaringe said. “We’re anticipating many hundreds of thousands of units of demand, ideally over a million units of demand across the globe. That means we will have at least two plants producing the vehicle.”

When Rivian hosted its first open house in the Normal town circle in fall 2019, the sprawling plant was still a hulking shell and empty parking lot overrun by geese. Now cranes are hovering over the factory in preparation for the retooling.

On Saturday, kids frolicked in the green and a few local merchants set up booths around Uptown Circle, while an amplified coffee-shop guitarist kept the vibe upbeat but mellow. In addition to the new models, Rivian also parked several R1 EVs on the circle, offering canned water from the ice-filled frunk of a $70,000 pickup truck. Nearby, attendees lined up for test drives in an R1.

The drivable R2 and R3 prototypes were for display purposes only.

The lanky, bespectacled Scaringe, his right arm in a sling from a mountain biking mishap, ambled through the crowd, casually greeting employees, customers and residents.

Reflecting on the open house five years ago, when he unveiled the first Rivian prototypes with little fanfare before the EV factory had been built, Scaringe, 41, thought about how far his auto company has come.

“I remember there were two cars — a truck and an SUV, early prototypes — and that was it,” Scaringe said. “And now there’s 100,000 vehicles on the road and we’re cranking one of those out every couple of minutes. It’s pretty wild.”

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    report r or r2

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  1. R vs. R-Squared: What's the Difference?

    R: The correlation between hours studied and exam score is 0.959. R2: The R-squared for this regression model is 0.920. This tells us that 92.0% of the variation in the exam scores can be explained by the number of hours studied. Also note that the R2 value is simply equal to the R value, squared: R2 = R * R = 0.959 * 0.959 = 0.920.

  2. How To Interpret R-squared in Regression Analysis

    R-squared is a goodness-of-fit measure for linear regression models. This statistic indicates the percentage of the variance in the dependent variable that the independent variables explain collectively. R-squared measures the strength of the relationship between your model and the dependent variable on a convenient 0 - 100% scale.

  3. Coefficient of Determination (R²)

    The coefficient of determination is a number between 0 and 1 that measures how well a statistical model predicts an outcome. The model does not predict the outcome. The model partially predicts the outcome. The model perfectly predicts the outcome. The coefficient of determination is often written as R2, which is pronounced as "r squared.".

  4. r² or R²

    r ranges from −1 to +1. Grey line is the line that fits the data the best. Image by author. If the points are very far away, r is close to 0 If the points are very close to the line and the line is sloping upward, r is close to +1 If the points are very close to the line and the line is sloping downward, r is close to −1 Notice how the figure above has missing numbers on the axes?

  5. How to Interpret Adjusted R-Squared and Predicted R-Squared in

    Now, onto which R-squared to report for what models. Typically, analysts will report the regular R-squared for the final model that a study settles on. ... I develop an nonlinear regression model in R studio with R2 (0.904), R2(adj) 0.864 and R2 (predicted) 0.919. I wonder if it is possible that predicted R2 higher than the normal R2? Hope for ...

  6. The Complete Guide to R-squared, Adjusted R-squared and Pseudo-R

    One of the most used and therefore misused measures in Regression Analysis is R² (pronounced R-squared). It's sometimes called by its long name: coefficient of determination and it's frequently confused with the coefficient of correlation r² . See it's getting baffling already! The technical definition of R² is that it is the proportion of variance in the response variable y that your ...

  7. Interpreting R²: a Narrative Guide for the Perplexed

    Photo by Josh Rakower on Unsplash. R² (R-squared), also known as the coefficient of determination, is widely used as a metric to evaluate the performance of regression models.It is commonly used to quantify goodness of fit in statistical modeling, and it is a default scoring metric for regression models both in popular statistical modeling and machine learning frameworks, from statsmodels to ...

  8. Relationship Between r and R-squared in Linear Regression

    When dealing with multiple linear regression: Y = β 0 + β 1 X 1 + β 2 X 2 + β 3 X 3 + β 4 X 4 + … + ε. R-squared will be the square of the correlation between the predicted/fitted values of the linear regression (Ŷ) and the outcome (Y): R 2 = Cor ( Ŷ, Y) 2. Note that in the special case of the simple linear regression:

  9. R-squared or coefficient of determination (video)

    In linear regression, r-squared (also called the coefficient of determination) is the proportion of variation in the response variable that is explained by the explanatory variable in the model. ... R2 only measures how well a line approximates points on a graph. It is NOT a probability value. How likely a model is correct depends on many ...

  10. R-Squared

    R-Squared (R² or the coefficient of determination) is a statistical measure in a regression model that determines the proportion of variance in the dependent variable that can be explained by the independent variable. In other words, r-squared shows how well the data fit the regression model (the goodness of fit). Figure 1.

  11. Coefficient of Determination (R Squared): Definition, Calculation

    Check out our tutoring page! Step 1: Find the correlation coefficient, r (it may be given to you in the question). Example, r = 0.543. Step 2: Square the correlation coefficient. Step 3: Convert the correlation coefficient to a percentage.

  12. Coefficient of determination

    In statistics, the coefficient of determination, denoted R2 or r2 and pronounced "R squared", is the proportion of the variation in the dependent variable that is predictable from the independent variable (s).

  13. How to interpret R Squared (simply explained)

    R Squared can be interpreted as the percentage of the dependent variable variance which is explained by the independent variables. Put simply, it measures the extent to which the model features can be used to explain the model target. For example, an R Squared value of 0.9 would imply that 90% of the target variance can be explained by the ...

  14. correlation

    You may want to give your non-statistical audience a sense of some rules of thumb set out by Cohen and others (something like r = .1 = small; r = .3 = medium; r = .5 = large), while at the same time telling them not to take such presciptions too literally.

  15. R-Squared: Definition, Calculation Formula, Uses, and Limitations

    R-squared is a statistical measure that represents the percentage of a fund or security's movements that can be explained by movements in a benchmark index. For example, an R-squared for a fixed ...

  16. How to Interpret Adjusted R-Squared (With Examples)

    The adjusted R-squared is a modified version of R-squared that adjusts for the number of predictors in a regression model. It is calculated as: Adjusted R2 = 1 - [ (1-R2)* (n-1)/ (n-k-1)] where: R2: The R2 of the model. n: The number of observations. k: The number of predictor variables. Because R-squared always increases as you add more ...

  17. R-squared vs Adjusted R-squared: Difference?

    Unlike the standard R-squared, which simply tells you the proportion of variance explained by the model, Adjusted R-squared takes into account the number of predictors (independent variables) in the model. The advantage of Adjusted R-squared is that it penalizes the inclusion of unnecessary variables.

  18. Reporting of R2 Statistics for Mixed-Effects Regression Models

    February 4, 2019. Reporting of R2 Statistics for Mixed-Effects Regression Models. Elias S. Sotirchos, MD 1; Kathryn C. Fitzgerald, ScD 1; Ciprian M. Crainiceanu, PhD 2. Author Affiliations Article Information. 1 Department of Neurology, Johns Hopkins University School of Medicine, Baltimore, Maryland. 2 Department of Biostatistics, Johns ...

  19. R Squared in R

    Thus, an R-squared model describes how well the target variable is explained by the combination of the independent variables as a single unit. The R squared value ranges between 0 to 1 and is represented by the below formula: R2= 1- SSres / SStot. Here, SSres: The sum of squares of the residual errors. SStot: It represents the total sum of the ...

  20. report package

    report. "From R to your manuscript". report 's primary goal is to bridge the gap between R's output and the formatted results contained in your manuscript. It automatically produces reports of models and data frames according to best practices guidelines (e.g., APA 's style), ensuring standardization and quality in results reporting.

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    Shoprite Group and four other leading global retailers yesterday said they had established a retail venture capital (VC) fund, W23 Global, to invest $125 million (R2.2 billion) over five years in ...

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    During the Triple Threat match for the United States Championship on Night 2 of WrestleMania 40 on Sunday, WWE Superstar Randy Orton had a run-in with popular…

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    Authorities on Monday reported traffic crashes and significant road delays across the country as thousands of people flocked to prime locations to gaze up at the rare solar eclipse. Local roads ...

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    The R2 is expected to go into production in the first half of 2026. When it does, it will be available in single-, dual- and tri-motor versions, the latter being able to do zero to 60 mph in under ...

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    President Joseph R. Biden, Jr. spoke today with President Xi Jinping of the People's Republic of China (PRC). The call follows the two leaders' meeting in Woodside, California in November 2023 ...

  26. Alienware m18 R2 review: A premium, beastly laptop for no-compromises

    There is a lot of variety in the Alienware m18 R2's price and performance, depending on the configuration you choose. The laptop starts at $1,900, and includes an Intel Core i7 processor, Nvidia ...

  27. AT&T data breach: Find out if you were affected

    Updated 2:32 PM PDT, March 31, 2024. NEW YORK (AP) — The theft of sensitive information belonging to millions of AT&T's current and former customers has been recently discovered online, the telecommunications giant said this weekend. In a Saturday announcement addressing the data breach, AT&T said that a dataset found on the "dark web ...

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  29. Rivian hosts R2 open house in Normal, its new production home

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