Function to calculate R2 (R-squared) in R

Function to calculate R2 (R-squared) in R

The R-squared (R²) statistic, also known as the coefficient of determination, is a measure of how much of the variability in the dependent variable can be explained by the independent variable(s) in a regression model. A high R-squared value indicates a good fit for the model, while a low R-squared value suggests that the model doesn't explain much variability.

In R, you can calculate R-squared in various ways depending on the context. Let's go over the following scenarios:

  1. Linear Regression with lm().
  2. Custom Function to Calculate R-squared.

1. Linear Regression with lm()

The simplest way to get R-squared in R is through the summary() function applied to a linear regression model created with lm(). Here's an example:

# Load necessary library # This is for plotting purposes only library(ggplot2) # Create sample data set.seed(42) # For reproducibility x <- rnorm(100) # Independent variable y <- 2 * x + rnorm(100) # Dependent variable # Fit a linear model model <- lm(y ~ x) # Get the summary of the model model_summary <- summary(model) # Extract R-squared r_squared <- model_summary$r.squared # Print R-squared print(paste("R-squared:", r_squared)) # Optional: Plot the data with the regression line ggplot(data = data.frame(x = x, y = y), aes(x = x, y = y)) + geom_point() + geom_abline(slope = coef(model)[2], intercept = coef(model)[1], color = "blue") + ggtitle(paste("Regression with R-squared:", round(r_squared, 3)))

2. Custom Function to Calculate R-squared

If you're interested in the formula for R-squared or need to calculate it manually for other reasons, here's a custom function that calculates R-squared:

# Custom function to calculate R-squared calculate_r_squared <- function(actual, predicted) { # Calculate total sum of squares ss_total <- sum((actual - mean(actual)) ^ 2) # Calculate residual sum of squares ss_residual <- sum((actual - predicted) ^ 2) # Calculate R-squared r_squared <- 1 - (ss_residual / ss_total) return(r_squared) } # Create sample data x <- rnorm(100) y <- 2 * x + rnorm(100) # Fit a linear model model <- lm(y ~ x) # Get the predicted values predicted <- predict(model) # Calculate R-squared using the custom function r_squared_custom <- calculate_r_squared(y, predicted) # Print R-squared print(paste("R-squared calculated manually:", r_squared_custom))

Explanation

  • Total Sum of Squares (SS Total): The total variance in the data. It's calculated by summing the squared differences between actual values and their mean.
  • Residual Sum of Squares (SS Residual): Variance not explained by the model. It's calculated by summing the squared differences between actual and predicted values.
  • R-squared Calculation: R2=1−SS TotalSS Residual​.

Using these approaches, you can calculate R-squared in R to evaluate the goodness-of-fit for linear regression models. You can also create custom functions to calculate R-squared based on specific requirements or additional regression contexts.

Examples

  1. "How to calculate R-squared in R using lm function"

    • Description: This query seeks to understand how to compute R-squared using the lm function, which is used for fitting linear models in R.
    • Code:
      # Fit a linear model model <- lm(y ~ x, data = dataset) # Calculate R-squared r_squared <- summary(model)$r.squared

  2. "R-squared calculation with residual sum of squares in R"

    • Description: This query aims to find the calculation method for R-squared involving residual sum of squares, a crucial component in the R-squared formula.
    • Code:
      # Fit a linear model model <- lm(y ~ x, data = dataset) # Calculate total sum of squares total_ss <- sum((dataset$y - mean(dataset$y))^2) # Calculate residual sum of squares residual_ss <- sum(residuals(model)^2) # Calculate R-squared r_squared <- 1 - (residual_ss / total_ss)

  3. "R2 calculation from scratch in R"

    • Description: This query is interested in understanding how to manually compute R-squared from scratch, without relying on built-in functions.
    • Code:
      # Calculate mean of dependent variable y y_mean <- mean(dataset$y) # Calculate total sum of squares total_ss <- sum((dataset$y - y_mean)^2) # Fit a linear model model <- lm(y ~ x, data = dataset) # Calculate residual sum of squares residual_ss <- sum(residuals(model)^2) # Calculate R-squared r_squared <- 1 - (residual_ss / total_ss)

  4. "Compute R2 using R-squared package in R"

    • Description: This query looks for a method to compute R-squared utilizing the functionalities of the R-squared package in R.
    • Code:
      # Install and load the R-squared package install.packages("R-squared") library(R-squared) # Fit a linear model model <- lm(y ~ x, data = dataset) # Calculate R-squared r_squared <- r2(model)

  5. "Calculate adjusted R-squared in R"

    • Description: This query seeks information on computing adjusted R-squared, a variation of R-squared that adjusts for the number of predictors in the model.
    • Code:
      # Fit a linear model model <- lm(y ~ x1 + x2 + x3, data = dataset) # Calculate adjusted R-squared adj_r_squared <- summary(model)$adj.r.squared

  6. "Formula for R2 in R linear regression"

    • Description: This query aims to find the mathematical formula used to calculate R-squared specifically in the context of linear regression in R.
    • Code:
      # Fit a linear model model <- lm(y ~ x, data = dataset) # Calculate R-squared r_squared <- summary(model)$r.squared

  7. "Calculate R2 with predictor and response variables in R"

    • Description: This query is interested in computing R-squared using both predictor and response variables within a dataset in R.
    • Code:
      # Fit a linear model model <- lm(response_variable ~ predictor_variable, data = dataset) # Calculate R-squared r_squared <- summary(model)$r.squared

  8. "R-squared calculation with ANOVA in R"

    • Description: This query seeks information on computing R-squared using ANOVA (Analysis of Variance) in R, which is a common method for assessing variance in linear models.
    • Code:
      # Fit a linear model model <- lm(y ~ x, data = dataset) # Perform ANOVA anova_result <- anova(model) # Extract R-squared from ANOVA table r_squared <- anova_result$'Sum Sq'[1] / sum(anova_result$'Sum Sq')

  9. "Calculate R-squared with non-linear regression in R"

    • Description: This query aims to understand how to compute R-squared when using non-linear regression models in R, which involve fitting curves instead of straight lines.
    • Code:
      # Fit a non-linear regression model model <- nls(y ~ f(x, theta), start = list(theta = initial_guess)) # Calculate R-squared r_squared <- 1 - (sum(residuals(model)^2) / sum((dataset$y - mean(dataset$y))^2))

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