1. Sherwin-Williams Company is attempting to develop a demand model for its line of exterior house paints. The company’s chief economist feels that the most important variables affecting paint sales (y) (measured in thousand gallons) are
Promotional expenditure (a) (measured in thousand dollars)
Selling price (p) (measured in dollars per gallon)
Disposable income per household (m) (measured in thousand dollars).
Using the variables specified by the Company’s chief economist, the Research Department obtained from a data set of 30 observations the following estimation result of a log-linear regression model given by .
| Coefficient Std. Err. t P>|t| [95% Conf. Interval]
| -.0232291 .1420415 -0.16 0.875 -.3707923 .324334
| -1.037375 .3655166 -2.84 0.030 -1.931762 -.1429884
| .3882373 .3753380 1.03 0.341 -.5301816 1.306656
constant | 6.951867 1.442853 4.82 0.003 3.421333 10.4824
First conduct an appropriate t-test for each independent variable except the constant as to whether it is statistically significant at the 95% confidence level, and then make an economic interpretation of each of the statistically significant coefficients. Use the “Students” probability distribution table for two tailed tests posted on the Blackboard (in the “Lecture Slides” folder).