You work for the children's division at Harley Davidson which produces a booster seat for infant motorcycle passengers ("Living High on the Hog!"). You've collected data on annual sales (S, number of booster seats sold per year) the price of your seat (P, in dollars), and the population size in the different cities in which your company has retail locations (N, number of people; you currently only have one establishment in each city). You estimate the following regression model: S = a + bP + cN. In your regressions, you usually look for a 5%-or-better level of confidence.

a. What signs do you expect for a, b, and c?

b. Your regression yields the following results:

Adjusted R Square	0.617
Independent Variables	Coefficients	Standard Error	t Stat	P-value
Intercept	5048	2013	2.508	0.05397
P	-66.37	18.72	-3.546	0.01647
N	0.0001	0.0056	0.026	0.97996

Interpret what these coefficients mean.

c. Does price have a statistically significant effect on sales?

d. Does population have a statistically significant effect on sales?

e. What portion of the total variation in sales remains unexplained?

f. Harley Davidson is considering selling booster seats in a new city, where the population is 176,000, and setting its booster seat price at $65. What level of annual sales would you expect in this new city (rounded to the nearest unit)?

Please provide explanations for each so I may compare with my answers too.