Question

You have fit a regression model with two regressors to a data set that has 20 observations. The total sum of squares is 1000 and the model (regression) sum of squares is 750. What is the adjusted R-squared value for this model

Answer 1

Hence the adjusted R-squared value for this model is 0.7205.

Explanation:

Given n= sample size=20

Total Sum of square (SST) =1000

Model sum of square(SSR) =750

Residual Sum of Square (SSE)=250

The value of R ^2 for this model is,

R^2 = \frac{SSR}{SST}

R^2 = 750/1000 =0.75

Adjusted
`R^2` :

`Adjusted R^2 =1- ((1-R^2)*(n-1))/((n-k-1))`

Where k= number of regressors in the model.

`Adjusted R^2 =1-(19* 0.25/((20-2-1)) = 0.7205`