THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A loan officer is interested in examining the determinants of the total dollar value of residential loans made during a month.She used Y = β 0 + β 1 X 1 + β 2 X 2 + β 3 X 3 + β 4

+ ε to model the relationship,where Y is the total dollar value of residential loans in a month (in millions of dollars),X 1 is the number of loans,X 2 is the interest rate,and X 3 is the dollar value of expenditures of the bank on advertising (in thousands of dollars).Suppose that by using data from the past 24 months,she obtained
= 3.8 + 0.23x 1 - 1.31x 2 + 0.032x 3 - 0.0005
.
-What do these results suggest about the relationship between the total loan amount and advertising?
A)As the amount of advertising increases,the total loan amount decreases at a decreasing rate.
B)As the amount of advertising increases,the total loan amount at first decreases,then increases.
C)As the amount of advertising increases,the total loan amount increases at an increasing rate.
D)As the amount of advertising increases,the total loan amount at first increases,then decreases.

Question

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A loan officer is interested in examining the determinants of the total dollar value of residential loans made during a month.She used Y = β 0 + β 1 X 1 + β 2 X 2 + β 3 X 3 + β 4

+ ε to model the relationship,where Y is the total dollar value of residential loans in a month (in millions of dollars),X 1  is the number of loans,X 2 is the interest rate,and X 3 is the dollar value of expenditures of the bank on advertising (in thousands of dollars).Suppose that by using data from the past 24 months,she obtained  
= 3.8 + 0.23x 1 - 1.31x 2 + 0.032x 3 - 0.0005  
.
-What do these results suggest about the relationship between the total loan amount and advertising?
A)As the amount of advertising increases,the total loan amount decreases at a decreasing rate. 
B)As the amount of advertising increases,the total loan amount at first decreases,then increases. 
C)As the amount of advertising increases,the total loan amount increases at an increasing rate. 
D)As the amount of advertising increases,the total loan amount at first increases,then decreases.

Quizplus · Accepted Answer

The coefficient for X₃ (the dollar value of expenditures on advertising) is positive, indicating that as the amount of advertising increases, the total loan amount at first increases. However, the coefficient is small (.032), and the negative quadratic coefficient (-.0005) indicates that as advertising continues to increase, the effect on total loans will eventually become negative. This suggests that there may be an optimal level of advertising spending that maximizes the total loan amount.