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# How to Calculate R-Squared by Hand

In statistics, R-squared (R2) measures the proportion of the variance in the response variable that can be explained by the predictor variable in a regression model.

We use the following formula to calculate R-squared:

R2 =Â  [ (nÎ£xy â€“ (Î£x)(Î£y)) / (âˆšnÎ£x2-(Î£x)2 * âˆšnÎ£y2-(Î£y)2) ]2

The following step-by-step example shows how to calculate R-squared by hand for a given regression model.

### Step 1: Create a Dataset

First, letâ€™s create a dataset:

### Step 2: Calculate Necessary Metrics

Next, letâ€™s calculate each metric that we need to use in the R2 formula:

### Step 3: Calculate R-Squared

Lastly, weâ€™ll plug in each metric into the formula for R2:

• R2 =Â  [ (nÎ£xy â€“ (Î£x)(Î£y)) / (âˆšnÎ£x2-(Î£x)2 * âˆšnÎ£y2-(Î£y)2) ]2
• R2 =Â  [ (8*(2169) â€“ (72)(223)) / (âˆš8*(818)-(72)2 * âˆš8*(6447)-(223)2) ]2
• R2 =Â  0.6686

Note: The n in the formula represents the number of observations in the dataset and turns out to be n = 8 observations in this example.

Assuming x is the predictor variable and y is the response variable in this regression model, the R-squared for the model is 0.6686.

This tells us that 66.86% of the variation in the variable y can be explained by variable x.