Question

3. You work for Mut the Custard, a frozen custard company. You’ve collected data on monthly sales (S, number of regular-sized frozen custards per month) the price of your regular-sized frozen custard (P, in dollars), and the population size in the different cities in which your company operates (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 10%-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 0.825 Independent Variables Coefficients Standard Error t Stat P-value Intercept 3510 639 5.494 0.00273 P -693.37 118.26 -5.863 0.00205 N 0.0176 0.0076 2.304 0.06943 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. Mut the Custard is considering selling in a new city, where the population is 63,000, and setting its regular-sized frozen custard price at $4.25. What level of monthly sales would you expect in this new city (rounded to the nearest unit)?

Answer 1

a) the expected sign would be positive sign for intercept a, negative sign for price coefficient b because when price increases demand decreases and sales falls, and positive sign for population coefficient c as population increases demand increases and sales rises.

b) the coefficient value of intercept is 3510 which shows at 0 price the autonomous sales is 3510 unit frozen costars. The price coefficient is -693.37 which show a one dollar in crease in price would reduce the sale of frozen costars is 693.37 unit. The increase in population by one unit will increase the sales by 0.0178 unit.

c) yes, price has a statistical significant effect on the sales as the p value is 0.00205 which is less then the 10 percent level of significance.

d) yes, population also has significant effect on sales as its p value is less then the value of level of significance. 0.06943 means 6%<10%.