How to Find Linear Regression in R

Updated 6 November 2026 · Standard formula, shown below

This guide shows you how to perform linear regression in R, from fitting a model with lm() to extracting coefficients, predictions, and diagnostics. You’ll enter your data, run a few commands, and get the regression equation, R-squared, and p-values that tell you how well your predictor explains the outcome.

What You’ll Need

R installed (version 4.0 or newer recommended) and preferably RStudio.
Your data in a format R can read: a CSV file, Excel file, or a built-in dataset.
Basic familiarity with R syntax (assigning variables, using functions).
No extra packages are required for simple linear regression; base R has everything.

Step-by-Step

Load your data into R. If you have a CSV file, use data <- read.csv("yourfile.csv"). For built-in datasets like mtcars, just type data(mtcars). Make sure your columns are numeric (use str(data) to check).
Check the relationship visually (optional but recommended). Run plot(y ~ x, data = data) where y is your outcome and x is your predictor. This helps spot non-linearity or outliers before fitting.
Fit the linear model. Use the lm() function: model <- lm(y ~ x, data = data). Replace y and x with your actual column names. For multiple predictors, add them with +: lm(y ~ x1 + x2, data = data).
View the model summary. Type summary(model) and press Enter. This gives you the coefficients (intercept and slopes), standard errors, t-values, p-values, and R-squared. The coefficient for x is the slope of the regression line.
Extract the coefficients directly. Use coef(model) to get just the intercept and slopes as a named vector. For example, coef(model)["x"] gives the slope.
Make predictions. For new data, create a data frame with the same predictor names: newdata <- data.frame(x = c(10, 20, 30)), then predict(model, newdata) to get predicted y-values.
Check model fit and assumptions. Run plot(model) to see residual plots. Look for a roughly horizontal line in the residuals vs. fitted plot and a normal Q-Q plot that follows the diagonal. These help validate that linear regression is appropriate.
Get confidence intervals for coefficients. Use confint(model) to see the 95% confidence intervals for the intercept and slopes. This tells you the range where the true coefficient likely lies.
Test if the overall model is significant. The F-statistic at the bottom of the summary output tests whether at least one predictor is useful. A p-value less than 0.05 (or your chosen threshold) indicates a significant model.
Export or report results. To save the coefficients, use write.csv(coef(model), "coefficients.csv"). For a quick report, you can copy the summary output into your document.

Common Mistakes

Using the wrong variable order in the formula. The syntax is y ~ x, not x ~ y. The outcome (dependent variable) goes on the left.
Forgetting to specify the data argument. If you omit data =, R looks for variables in the global environment, which may cause errors or use the wrong columns.
Interpreting the intercept incorrectly. The intercept is the predicted y when all x are 0. If 0 is not meaningful for your predictor, the intercept may not be practically useful.
Ignoring non-linear patterns. If your scatterplot shows a curve, a straight line may not fit well. Consider polynomial terms or transformations.
Using summary() but not checking the residual standard error. The residual standard error (RSE) tells you the typical distance of points from the regression line; a large RSE relative to the mean of y indicates poor fit.

Tips

Always start with a plot. It takes seconds and can reveal issues that numbers alone will hide.
Use names(model) to see all the components you can extract, like fitted.values and residuals.
Standardize your predictors if they have very different scales, especially for multiple regression, to make coefficient comparisons easier.
Check for multicollinearity in multiple regression using car::vif(model) (requires the car package).
Save your model with saveRDS(model, "model.rds") so you can load it later with readRDS() without refitting.

Troubleshooting

Error: “object ‘y’ not found” – This usually means you didn’t specify data = or the column name is misspelled. Check with names(data).
Error: “NAs are not allowed” – Your data has missing values. Remove them with na.omit(data) or use na.action = na.exclude in lm().
Warning: “essentially perfect fit” – This happens when your predictor perfectly predicts the outcome (e.g., you accidentally included the outcome as a predictor). Double-check your formula.
Summary shows NA for a coefficient – This often indicates perfect multicollinearity (one predictor is a linear combination of others). Remove redundant predictors.
Predictions are wildly off – Check that your new data has the same column names and types as the training data. Use str() to compare.

Frequently Asked Questions

How do I get the equation of the regression line?

Use coef(model) to get the intercept and slope. The equation is y = intercept + slope * x. For example, if intercept is 2 and slope is 3, the line is y = 2 + 3x.

What does R-squared mean?

R-squared is the proportion of variance in the outcome explained by the predictors. A value of 0.8 means 80% of the variability in y is explained by the model. It ranges from 0 to 1, but a high value doesn’t guarantee the model is appropriate.

How do I add a regression line to a scatterplot?

After plotting, use abline(model) to add the fitted line. For a smoother curve, use lines(fitted(model) ~ x, data).

Can I do linear regression with multiple predictors?

Yes, just add them in the formula: lm(y ~ x1 + x2 + x3, data = data). The summary will show a coefficient for each predictor, and the F-test tests the overall model.

What if my data is not linear?

Try transformations like log(y) or sqrt(x), or add polynomial terms like lm(y ~ x + I(x^2)). Check the residual plots to see if the fit improves.

How do I export the regression results?

Use sink("output.txt") then summary(model) then sink() to save the output to a file. For a tidy table, consider the broom package’s tidy(model).

Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.