Can You Calculate R Squared Without N

What is R-Squared?

R-squared, or the coefficient of determination, measures how well a regression model fits the observed data. It compares the explained variation to the total variation in the dependent variable. A higher R-squared value indicates a better fit of the model to the data.

R-squared is calculated by dividing the explained sum of squares by the total sum of squares. The explained sum of squares represents the variation explained by the regression model, while the total sum of squares represents the total variation in the dependent variable.

Calculating R-Squared

To calculate R-squared, you need the following components:

• Sum of squares due to regression (SSR)
• Sum of squares due to error (SSE)
• Total sum of squares (SST)

The formula for R-squared is:

Where:

• SSR = Explained sum of squares
• SST = Total sum of squares = SSR + SSE

Can You Calculate R-Squared Without N?

Yes, you can calculate R-squared without knowing the sample size (N) directly. The sample size is not required in the R-squared formula because it cancels out during the calculation. Instead, you need the sums of squares (SSR and SST) or the variance components.

R-squared is a ratio of sums of squares, not a function of N. Therefore, as long as you have the necessary sums of squares, you can compute R-squared without needing to know N.

The Formula

The R-squared formula is:

Where:

• SSE = Sum of squares due to error
• SST = Total sum of squares

Alternatively, you can use the SSR version:

Both formulas are equivalent because SST = SSR + SSE.

Worked Example

Let's calculate R-squared for a simple linear regression model where:

• SSR = 180
• SSE = 60

First, calculate SST:

Then, calculate R-squared using the SSR version:

This means 75% of the variance in the dependent variable is explained by the independent variable(s).