In a multiple regression problem involving 24 observations and three independent variables, the estimated regression equation is $ = 72 + 3.2 x _ { 1 } + 1.5 x _ { 2 } - x _ { 3 }$ . For this model, SST = 800 and SSE = 245. The value of the F-statistic for testing the significance of this model is 15.102.

Question

In a multiple regression problem involving 24 observations and three independent variables, the estimated regression equation is $ = 72 + 3.2 x _ { 1 } + 1.5 x _ { 2 } - x _ { 3 }$  . For this model, SST = 800 and SSE = 245. The value of the F-statistic for testing the significance of this model is 15.102.

Quizplus · Accepted Answer

The F-statistic is calculated as (SSR/k) / (SSE/(n-k-1)), where SSR is the sum of squares due to regression, k is the number of independent variables, SSE is the sum of squares due to error, and n is the number of observations. Given SST = SSR + SSE, we can calculate SSR as SST - SSE, which gives us SSR = 555. Thus, the F-statistic is (555/3)/(245/20) = 15.102. This matches the given value, so the answer is A.

In a Multiple Regression Problem Involving 24 Observations and Three =72+3.2x1+1.5x2−x3 = 72 + 3.2 x _ { 1 } + 1.5 x _ { 2 } - x _ { 3 }=72+3.2x1​+1.5x2​−x3​

In a Multiple Regression Problem Involving 24 Observations and Three $= 72 + 3.2 x _ { 1 } + 1.5 x _ { 2 } - x _ { 3 }$