You work for a snow cone company. You've collected data on monthly sales (S, number of snow-cones per month) and the price of your regular-size snow-cone (P, in dollars), as well as the daily average summer temperature in your most popular market (T, in degrees Fahrenheit). You estimate the following regression model:
S = a + bP + cT.
In your regressions, you usually look for a 10%-or-better level of confidence.
a) What are the expected signs for a, b, and c?
Your regression yields the following results:
Adjusted R Square 0.883
Independent Variables Coefficients Standard Error t Stat P-value
Intercept 2718 598 4.544 0.00615
P -641.62 90.23 -7.111 0.00085
T 10.32 6.36 1.623 0.16562
b) The estimated coefficient for a (intercept) suggests that?
c) The estimated coefficient for b (price of the regular size snow-cone) suggests that?
d) The estimated coefficient for c (daily average summer temperature) suggests that?
e) The price of the regular size snow-cone has a statistically significant effect on our sales? True or False
f) Daily average summer temperature affects the sales of regular size snow-cones in a statistically significant way? True or False
g) What portion of the total variation in sales of the regular size snow-cone remains unexplained?
h) The snow cone company is considering selling in a new city, where the average daily summer temperature is 83°, for a price of $4.10. What level of sales would you expect in this new city (rounded to the nearest unit)?