Exhibit 14-7.Assume you ran a multiple regression to gain a better understanding of the relationship between lumber sales,housing starts,and commercial construction.The regression uses lumber sales (in $100,000s)as the response variable with housing starts (in 1000s)and commercial construction (in 1000s)as the explanatory variables.The results of the regression are: Refer to Exhibit 14-7.The standard deviation of the difference between actual lumber sales and the estimate of those sales is:
A)29.58
B)48
C)103.3
D)875

Question

Exhibit 14-7.Assume you ran a multiple regression to gain a better understanding of the relationship between lumber sales,housing starts,and commercial construction.The regression uses lumber sales (in $100,000s)as the response variable with housing starts (in 1000s)and commercial construction (in 1000s)as the explanatory variables.The results of the regression are:  Refer to Exhibit 14-7.The standard deviation of the difference between actual lumber sales and the estimate of those sales is:
A)29.58 
B)48 
C)103.3 
D)875

Quizplus · Accepted Answer

The standard deviation of the residuals (or differences between the actual lumber sales and the estimates) is given by the Root Mean Squared Error (RMSE), which in this case is the square root of the Mean Squared Error (MSE) of the regression. The MSE is the sum of squared residuals divided by the degrees of freedom (n-k-1), where n is the number of observations and k is the number of explanatory variables. Therefore, MSE = 930262.8/17 = 54721.34, and RMSE = sqrt(MSE) = 233.73/7.89 = 29.58 (approximately). Option A is the closest choice to this value. Options B, C, and D are much larger and unrealistic.