You work at a company (Freeze Your Butt On ®) that produces window air condition
ID: 3247511 • Letter: Y
Question
You work at a company (Freeze Your Butt On®) that produces window air conditioning units. To gauge performance, you’ve utilized data on monthly sales (S) and the price of your most popular unit (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
0.425
Coefficients
Standard Error
t Stat
P-value
Intercept
131768
50048
2.633
0.04638
P
-70.91
28.97
-2.448
0.05810
T
912.53
651.09
1.402
0.21997
Interpret what these coefficients mean.
c. Does our price have a statistically significant effect on our sales?
d. Does average temperature have a statistically significant effect on our sales?
e. What fraction of the total variation in our sales remains unexplained?
f. Our company is considering selling our most popular unit in a new city, where the average daily summer temperature is 72°, for a price of $325. What level of sales would you expect in this new city (rounded to the nearest dollar)?
Adjusted R Square
0.425
Coefficients
Standard Error
t Stat
P-value
Intercept
131768
50048
2.633
0.04638
P
-70.91
28.97
-2.448
0.05810
T
912.53
651.09
1.402
0.21997
Explanation / Answer
a. Sign of intercept should be positive as Sales can't be negative when both price of most popular product and summer temperature is 0 unit. So sign of 'a' is positive. Now Monthly sale should increase if price of the most popular unit decreases. So the sign of 'b' will be negative. Again monthly sale icreases significantly if daily average summer temperature increases. So the sign of 'c' should be positive quite evidently.
b. Intercept value of 131768 implies when price of most popular unit is 0 dollar and average summer temperature is 0° F, then sales will be 131768 dollar monthly.
Co-efficient value of -70.91 corresponding to sales of most popular product implies one dollar increase of price of most popular product will result in decrease of 70.91 dollars in total monthly sales.
Co-efficient value of 912.53 corresponding to average summer temperature implies, 1°F temperature increase will increase the sales by 912.53 dollars.
c. Here level of significance is 10% or 0.1.
p-value corresponding to price is 0.05810, which is less than 0.1. Hence, Price have a statistically significant effect on sales.
d. p-value corresponding to average daily temperature is 0.21997, which is greater than 0.1.
Hence total temperature doesn't have a statistically significant effect on sales.
e. If we assume Adjusted R-square and predicted R-square are similar in this case, then proportion of total Variation of sales explained by the model = 0.425 i.e. 42.5%.
Hence proportion of unexplained variation in sales = 1 - 0.425 = 0.575 i.e. 57.5%. (Ans).
f. Expected sales from the regression equation =
131768 - ( 70.91 * 325) + (912.53 * 72) = 174424.41 dollars. (Ans).
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