Calculate R2 For Each Variable In R

Use this interactive calculator to convert correlation coefficients into R² values for each predictor, estimate the percentage of variance explained, and generate a clean visual comparison you can reproduce in R.

R² Calculator

R² Comparison Chart

The chart compares the variance explained by each predictor. For a simple bivariate relationship, R² is calculated as r × r. The sign of r affects direction, but not R² magnitude.

How to Calculate R² for Each Variable in R

When analysts say they want to calculate R² for each variable in R, they are usually talking about one of two related tasks. First, they may want to take the correlation between a predictor and an outcome, then square that correlation to get the proportion of variance explained by that single variable. Second, they may want to inspect how much explanatory power each variable contributes within a regression workflow. The most direct interpretation starts with the first case: if you know a variable’s correlation coefficient, r, then the coefficient of determination for that one-variable relationship is simply R² = r².

This sounds simple, but it matters a great deal in practice. A predictor with a correlation of 0.20 explains only 4% of variance. A predictor with a correlation of 0.70 explains 49% of variance. That difference is huge, and it shows why squaring the correlation is such a useful way to compare practical importance. In R, this can be done with a single expression, but understanding the logic behind the number helps you interpret outputs correctly and avoid common mistakes.

What R² Means for an Individual Variable

R² measures the proportion of variability in a dependent variable that is explained by a predictor. In a simple linear regression with one predictor, R² is exactly equal to the square of Pearson’s correlation coefficient between x and y. If a variable has r = -0.80 with the outcome, then R² = 0.64. The negative sign disappears after squaring, because R² reflects explanatory strength, not direction.

• r describes direction and strength of the linear relationship.
• R² describes how much variance is explained.
• Percent variance explained is simply R² × 100.

That means two variables can have correlations of +0.60 and -0.60 and both produce the same R² of 0.36. They explain the same amount of variance, even though one is positively associated and the other is negatively associated with the outcome.

Basic R Code to Calculate R² for Each Variable

Suppose your dependent variable is y and your predictors are stored in a data frame called df. If you want to calculate the bivariate R² for each predictor, one simple strategy is to compute the correlation between each predictor and y, then square it.

cors <- sapply(df[, c(“x1”, “x2”, “x3”)], function(x) cor(x, df$y, use = “complete.obs”)) r2_values <- cors^2 r2_values

This approach is transparent and fast. It is especially useful in exploratory analysis, feature screening, educational settings, or when you need a quick ranking of variables by explanatory strength. It also works well when predictors are measured on different scales, because correlation is scale-independent.

Example with Real Statistics from the mtcars Dataset

The built-in mtcars dataset is a classic demonstration set in R. Correlations between mpg and several variables are well known and illustrate how single-variable R² values can differ sharply. Here is a practical comparison.

Variable	Correlation with mpg (r)	R² = r²	Variance Explained
wt	-0.868	0.753	75.3%
disp	-0.848	0.719	71.9%
hp	-0.776	0.602	60.2%
qsec	0.419	0.176	17.6%

This table shows why analysts often compute R² for each variable before fitting larger models. Weight and displacement each explain a substantial share of variance in fuel economy on their own, while quarter-mile time explains much less. However, the moment you move to multiple regression, shared information between predictors becomes important. Variables like wt and disp are related to one another, so their individual bivariate R² values cannot simply be added together.

Bivariate R² Versus Multiple Regression R²

One of the biggest sources of confusion is the difference between individual-variable R² and model R². If you run separate one-predictor regressions, each model gets its own R². But if you fit a single model with many predictors, the model has one overall R² that reflects the combined explanatory power of all included variables. Inside a multiple regression, a variable’s unique contribution is better described through semi-partial correlation, partial R², nested model comparison, or variable importance metrics.

Use bivariate R² when:

• You want a fast screen of predictor strength.
• You are teaching or learning the connection between r and R².
• You are working with one predictor at a time.
• You need an interpretable variance-explained metric for each variable individually.

Use partial or model-based methods when:

• You need the unique effect of a predictor controlling for others.
• Your predictors are correlated with one another.
• You are evaluating feature importance in a multiple regression.
• You need inferential statistics for nested models.

Calculating R² for Each Variable Using a Loop in R

If you prefer a formula-based workflow, you can also fit a separate regression for each predictor and extract the R² from the model summary. This returns the same answer as squaring the correlation in standard simple linear regression.

predictors <- c(“x1”, “x2”, “x3”) r2_each <- sapply(predictors, function(v) { formula_obj <- as.formula(paste(“y ~”, v)) summary(lm(formula_obj, data = df))$r.squared }) r2_each

This strategy is useful when you want consistency with a modeling pipeline or when you plan to extend the process to adjusted R², p-values, confidence intervals, or diagnostics.

Real Example from the iris Dataset

Another familiar example comes from the classic iris dataset. If the outcome is Sepal.Length, then some predictors explain much more variation than others.

Variable	Correlation with Sepal.Length (r)	R² = r²	Variance Explained
Petal.Length	0.872	0.760	76.0%
Petal.Width	0.818	0.669	66.9%
Sepal.Width	-0.118	0.014	1.4%

This type of summary is effective because it immediately separates strong signals from weak ones. In practice, a predictor with a very low R² might still matter in a multivariable model, but as a standalone relationship it does not explain much variation.

Step-by-Step Interpretation

1. Compute the correlation coefficient between a predictor and the outcome.
2. Square the correlation value.
3. Interpret the squared value as the proportion of variance explained.
4. Multiply by 100 if you want a percentage.
5. Compare variables side by side, but remember not to add their R² values together in a correlated predictor set.

For example, if cor(df$x1, df$y) = 0.45, then the variable’s R² is 0.2025. That means x1 explains about 20.25% of the variance in y in a simple linear relationship.

Common Mistakes to Avoid

• Confusing sign with explanatory power: a negative correlation can still produce a high R².
• Adding R² values across predictors: overlapping information means bivariate R² values are not additive.
• Using the wrong missing-data rule: in R, specify use = "complete.obs" or a similar method when correlations contain missing values.
• Assuming causation: a high R² indicates fit, not proof of a causal mechanism.
• Ignoring nonlinear structure: r and R² from simple linear models may understate important curved relationships.

How to Calculate R² for Every Numeric Variable Automatically

If your dataset contains many numeric columns, you can automate the process. A common workflow is to select numeric variables, exclude the target, compute all correlations against the target, and square the result. Here is an efficient pattern in base R.

num_df <- df[sapply(df, is.numeric)] target <- “y” predictor_names <- setdiff(names(num_df), target) r_vals <- sapply(num_df[predictor_names], function(x) cor(x, num_df[[target]], use = “complete.obs”)) r2_vals <- sort(r_vals^2, decreasing = TRUE) r2_vals

This kind of ranking is especially helpful at the beginning of a predictive modeling project. It gives you a defensible first look at which variables deserve closer attention.

When to Report Adjusted R² Instead

For a single predictor, ordinary R² is usually sufficient. But in multiple regression, adjusted R² is often more informative because it penalizes model complexity. If your goal is truly “for each variable,” then bivariate R² remains the clearest variable-level measure. If your goal is “for each variable while controlling for others,” then you should look beyond ordinary R² and consider partial R², change in R² from nested models, or ANOVA model comparison.

Useful References and Authoritative Sources

For deeper statistical background and applied guidance, consult these authoritative resources:

• NIST Engineering Statistics Handbook
• Penn State STAT 462: Applied Regression Analysis
• UCLA Statistical Methods and Data Analytics for R

Practical Takeaway

To calculate R² for each variable in R, the most direct method is to compute each variable’s correlation with the outcome and square it. This yields a clean, interpretable proportion of variance explained for each predictor considered alone. It is easy to implement, fast to communicate, and ideal for quick comparisons. Just remember the key limitation: these are individual explanatory measures, not unique contributions within a multivariable model.

If you need a simple rule of thumb, think of the workflow like this: use correlation squared for standalone variable strength, and use nested models or partial statistics for unique multivariable contribution. That distinction will keep your interpretation both statistically correct and practically useful.