In a multiple regression problem involving 24 observations and three independent variables, the estimated regression equation is $\hat { y }$ = 72 + 3.2x1 + 1.5 x2 - x3. 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

Quizplus · Accepted Answer

The F-statistic in a multiple regression model is calculated using the formula $F = \frac{MSR}{MSE}$, where $MSR = \frac{SSR}{df_{regression}}$ and $MSE = \frac{SSE}{df_{error}}$. SSR (Sum of Squares due to Regression) can be found as $SST - SSE$. Given SST = 800 and SSE = 245, SSR = 800 - 245 = 555. With 3 independent variables, $df_{regression} = 3$ and $df_{error} = 24 - 3 - 1 = 20$, so $MSR = \frac{555}{3}$ and $MSE = \frac{245}{20}$. Plugging these into the formula for F gives an F-statistic that matches the provided value when calculated correctly, confirming the statement is true.

In a Multiple Regression Problem Involving 24 Observations and Three y^\hat { y }y^​

In a Multiple Regression Problem Involving 24 Observations and Three $\hat { y }$