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

Answer:

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

Step-by-step 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 $R^2$ :

$Adjusted R^2 =1- \frac{(1-R^2)\times(n-1)}{(n-k-1)}$

Where k= number of regressors in the model.

$Adjusted R^2 =1-(19\times 0.25/((20-2-1)) = 0.7205$