The following regression was estimated for 45 quarters to test the hypothesis th
ID: 1250715 • Letter: T
Question
The following regression was estimated for 45 quarters to test the hypothesis that tire sales (T) depend on new-automobile sales (A) and total miles driven (M)T = 0.45 + 1.41 (M) + 1.12 (A)
(0.32) (0.19) (0.41)
Where T is the % change in tire sales, M is the % change in miles driven, and A is the % change in new automobile sales. N=23, and R square = 0.83, the standard error of the regression = 1.2 and standard errors for the coefficients are listed in parentheses.
a) does the regression equation and its coefficients make economic sense? Explain.
b) Suppose "miles driven" is expected to fall by 2% and new auto sales to fall by 13% (due to forecast recession). What is the predicted change in the sales quantity of tires? If actual tire sales dropped by 18% would this be surprising?
Explanation / Answer
a) Sure, the more cars there are out there (new auto sales) and the more miles they are driven (more wear and tear on tires) the higher the demand for new tires. b) T= 0.45 +1.41 (-2) + 1.12 (-13)= -16.93. No, if they dropped 18% this is only (18-16.93)/1.2= 0.89 standard errors away from the predicted mean. P value is .1869 so this or more would happen nearly 20% of the time.