Question

You work for Segway, in the sales division of the One S1 (which is basically a motorized unicycle without the seat). You’ve collected data on monthly sales (S) and the price of the One S1 (P), both 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 signs do you expect for a, b, and c?

b.   Your regression yields the following results:

Adjusted R Square	0.733
Independent Variables	Coefficients	Standard Error	t Stat	P-value
Intercept	51165	4980	10.275	0.00015
P	-38.50	8.42	-4.573	0.00598
T	29.07	32.56	0.893	0.41285

      Interpret what these coefficients mean.

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

d.   Does average temperature have a statistically significant effect on sales?

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

f.    Our company is considering selling our most popular unit in a new city, where the average daily summer temperature is 65°, for a price of $570. What level of sales would you expect in this new city (rounded to the nearest dollar)?

Answer 1

a) I would expect a positive sign for a that is the intercept. Even when no variable have effect there should be some amount of sales hence a positive sigh. B should be negative as it is the price. When price increase the demand decrease and hence the sales will also decrease. C will be positive sigh as the temperature is positively related to the sales of the bike.

b) The coefficient mean that 51165 sales will be there when there is not variable effect. When price P increase by 1 unit then the sales decrease by 38.5 units. And when T increase by 1 unit then the Sales increase by 29.07 unit.

c) To check this we need to see the Pvalue. When the p value is less that 0.1 then it is called that the variable is significant. Over here the P value of Price P is .00598 which is definately less than 0.1 so we can say itis significant.

d) It also significant as P value of T is less tha 0.1

e) R sq tell us about the total variation in sales remains explained. So to find the unexplained we need to do 1-Rsq= 1-.733= .267

f) Puth the value of P and T in the regression equation and find the sales.