In a regression analysis involving 30 observations the follo

In a regression analysis involving 30 observations, the following estimated regression equation was obtained.

y ˆ = 17.6 + 3.8x1 - 2.3x2 + 7.6x3 + 2.7x4

Suppose x1 and x4 are dropped from the model and the following estimated regression equation is obtained.

y ˆ = 11.1 - 3.6x2 + 8.1x3

For this model SST = 1805 and SSR = 1705.

Compute SSE for this model.
  

Use an F test and = .05 to determine whether x1 and x4 contribute significantly to the model.

What is the value of the F test statistic (to 2 decimals)?
  

What is the p-value?
Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 9  

What is your conclusion about the two variables x1 and x4?
SelectConclude that these variables contribute significantly to the modelCannot conclude that these variables contribute significantly to the modelItem 10

Solution

a. SSE = SST - SSR = 1,805 - 1,780 = 25

MSR = SSR/(k) = 1,780/4 = 445

MSE = SSE/(n-k-1) = 25/25 = 1

F = MSR/MSE = 445/1 = 445

Associated p-value = 0.000

At 5% los, critical value = 2.759 < F, hence Conclude that the relationship is significant.

Now,

SSE = SST - SSR = 1805-1705 = 100

F= (1705/2)/(100/27) = 230.175

Associated p-value = 0.000

At 5% los, critical value = 3.354 < F, hence Conclude that these variables contribute significantly to the model.