What does an r-squared value of 0.3 mean

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 =  [ (nΣxy – (Σx)(Σy)) / (√nΣx²-(Σx)² * √nΣy²-(Σy)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, let’s create a dataset:

Step 2: Calculate Necessary Metrics

Next, let’s calculate each metric that we need to use in the R² formula:

Step 3: Calculate R-Squared

Lastly, we’ll plug in each metric into the formula for R²:

• R² =  [ (nΣxy – (Σx)(Σy)) / (√nΣx²-(Σx)² * √nΣy²-(Σy)²) ]²
• R² =  [ (8*(2169) – (72)(223)) / (√8*(818)-(72)² * √8*(6447)-(223)²) ]²
• R² =  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 th

how to find r 2 in stats

how to find r 2 in stats calculator