Exhibit 16-1
In a regression analysis involving 25 observations, the following estimated regression equation was developed. = 10 - 18x 1 + 3x 2 + 14x 3
Also, the following standard errors and the sum of squares were obtained.S b1 = 3 S b2 = 6 S b3 = 7
SST = 4,800 SSE = 1,296
-Refer to Exhibit 16-1. The model
A)is significant
B)is not significant
C)may or may not be significant
D)None of these alternatives is correct.

Question

Exhibit 16-1
In a regression analysis involving 25 observations, the following estimated regression equation was developed.  = 10 - 18x 1 + 3x 2 + 14x 3 
Also, the following standard errors and the sum of squares were obtained.S b1 = 3 S b2 = 6 S b3 = 7
SST = 4,800 SSE = 1,296
-Refer to Exhibit 16-1. The model
A)is significant 
B)is not significant 
C)may or may not be significant 
D)None of these alternatives is correct.

Quizplus · Accepted Answer

To determine if the model is significant, we need to conduct an F-test. The F-statistic is calculated as (SSR/k)/(SSE/(n-k-1)), where SSR is the regression sum of squares, k is the number of independent variables (excluding the intercept), SSE is the error sum of squares, and n is the sample size. Using the information provided, we can calculate SSR as SST - SSE = 4,800 - 1,296 = 3,504 and k as 3 (since there are 3 independent variables). Therefore, the F-statistic is (3,504/3)/(1,296/21) = 36. Since this F-statistic exceeds the critical value at a significance level of 0.05, we reject the null hypothesis that the model is not significant and conclude that the model is significant.

Exhibit 16-1 In a Regression Analysis Involving 25 Observations, the Following Estimated