Question

regression model involving 4 independent variables and a sample of 15 observations resulted in the following sum of squares. SSR = 165 SSE = 60 The multiple coefficient of determination is a. .5. b. .7333. c. .275. d. .3636.

Answer 1

The multiple coefficient of determination is b. .7333

Explanation:

The coefficient of determination, denoted as R², is defined as follows:

R² = SSR / SST

where

• SSR is the regression sum of squares
• SST is the total sum of squares

Since we are given SSR and SSE, we can calculate SST by using the equation

SSE = SST - SSR

where

• SSE is the Error in the sum of squares

Thus,

SST = SSE + SSR

= 60 +165

= 225

Therefore,

R² = SSR / SST

R² = 165 / 225

R² = 0.7333

Therefore, the multiple coefficient of determination is 0.7333