Task: Regression and Price Elasticity
Question: The Pilot Pen Company has decided to use 15 test markets to examine the sensitivity of demand for its new product to various prices, as shown in the following table. Advertising effort was identical in each market. Each market had approximately the same level of business activity and population.
1) Using a linear regression model, estimate the demand function for Pilot's new pen.
2) Evaluate this model by computing the coefficient of determination and by performing a t-test of the significance of the price variable.
3) What is the price elasticity of demand at a price of 50 cents?
| Test Market |
Price Charged |
Quantity Sold (thousands of pens) |
| 1 |
50¢ |
20.0 |
| 2 |
50¢ |
21.0 |
3
|
55¢ |
19.0 |
| 4 |
55¢ |
19.5 |
| 5 |
60¢ |
20.5 |
| 6 |
60¢ |
19.0 |
| 7 |
65¢ |
16.0 |
| 8 |
65¢ |
15.0 |
| 9 |
70¢ |
14.5 |
| 10 |
70¢ |
15.5 |
| 11 |
80¢ |
13.0 |
| 12 |
80¢ |
14.0 |
| 13 |
90¢ |
11.5 |
| 14 |
90¢ |
11.0 |
| 15 |
40¢ |
17.0 |