Exhibit 13-3 In a regression model involving 30 observations, the following estimated regression equation was obtained: = 17 + 4x 1 - 3x 2 + 8x 3 + 8x 4 For this model SSR = 700 and SSE = 100. -Refer to Exhibit 13-3. The conclusion is that the A)model is not significant B)model is significant C)slope of x₁ is significant D)slope of x₂ is significant

Question

Quizplus · Accepted Answer

SSR = 700 and SSE = 100, therefore, total sum of squares (SST) = SSR + SSE = 800. 
To determine if the model is significant, we can perform an F-test using the following formula: 
F = MSR/MSE = SSR/df(regression) / SSE/df(error) 
where MSR = mean sum of squares of regression and MSE = mean sum of squares of error. 
df(regression) = number of independent variables in the model = 4 
df(error) = n- k -1 = 30 - 4 - 1 = 25 
Plugging in the values, we get: 
F = SSR/df(regression) / SSE/df(error) = 700/4 / 100/25 = 43.75 
Using an F-distribution table with degrees of freedom (4,25), we find the critical value at α=0.05 to be 2.86. 
Since the calculated F-value (43.75) is much greater than the critical value (2.86), we reject the null hypothesis and conclude that the model is significant. 
We cannot make any conclusion about the significance of individual slopes without conducting t-tests on each of them.

Exhibit 13-3 In a Regression Model Involving 30 Observations, the Following Estimated