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. Complete the following worksheet and then estimate the demand function for Pilot's new pen using a linear regression model. Test Market Price Charged Quantity Sold (cents) (Thousands of Pens) ii xixi yiyi xixiyiyi xi2xi2 yi2yi2 1 50 20 1,000 2,500 400 2 50 21 1,050 2,500 441 3 55 19 1,045 3,025 361 4 55 19.5 1,072.5 3,025 380.25 5 60 20.5 1,230 3,600 420.25 6 60 19 1,140 3,600 361 7 65 15.5 1,007.5 4,225 240.25 8 65 15 975 4,225 225 9 70 14.5 1,015 4,900 210.25 10 70 15.5 1,085 4,900 240.25 11 80 13 1,040 6,400 169 12 80 14 1,120 6,400 196 13 90 11.5 1,035 8,100 132.25 14 90 11 990 8,100 121 15 40 17 680 1,600 289 Total 980 246 ? 67,100 ? Regression Parameters Estimations Slope (ββ) ? Intercept (αα) ? What is the standard error of the estimate (sese)? 1.754 1.532 105.182 What is the estimate of the standard deviation of the estimated slope (sbsb)? 1.897 0.028 0.032 Can you reject the hypothesis (at the 0.05 level of significance) that there is no relationship (i.e., β=0β=0) between the price and quantity variables? (Hint: t0.025,13=2.16t0.025,13=2.16) Yes No Complete the following worksheet and then use it to calculate the coefficient of determination. ii xixi yiyi yˆy^ (yˆi−y¯)2y^i−y¯2 (yi−y¯)2yi−y¯2 1 50 20 19.329 8.579 12.960 2 50 21 19.329 8.579 21.160 3 55 19 18.374 3.897 6.760 4 55 19.5 18.374 3.897 9.610 5 60 20.5 17.419 1.038 16.810 6 60 19 17.419 1.038 6.760 7 65 15.5 16.464 0.004 0.810 8 65 15 16.464 0.004 1.960 9 70 14.5 15.509 0.794 3.610 10 70 15.5 15.509 0.794 0.810 11 80 13 13.599 7.846 11.560 12 80 14 13.599 7.846 5.760 13 90 11.5 11.689 22.194 24.010 14 90 11 11.689 22.194 29.160 15 40 17 21.239 23.416 0.360 Total ? ? The coefficient of determination (r2r2) is? What is the price elasticity of demand at a price of 50 cents? -0.50 -0.46 -0.02 0.03

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. Complete the following worksheet and then estimate the demand function for Pilot's new pen using a linear regression model. Test Market Price Charged Quantity Sold (cents) (Thousands of Pens) ii xixi yiyi xixiyiyi xi2xi2 yi2yi2 1 50 20 1,000 2,500 400 2 50 21 1,050 2,500 441 3 55 19 1,045 3,025 361 4 55 19.5 1,072.5 3,025 380.25 5 60 20.5 1,230 3,600 420.25 6 60 19 1,140 3,600 361 7 65 15.5 1,007.5 4,225 240.25 8 65 15 975 4,225 225 9 70 14.5 1,015 4,900 210.25 10 70 15.5 1,085 4,900 240.25 11 80 13 1,040 6,400 169 12 80 14 1,120 6,400 196 13 90 11.5 1,035 8,100 132.25 14 90 11 990 8,100 121 15 40 17 680 1,600 289 Total 980 246 ? 67,100 ? Regression Parameters Estimations Slope (ββ) ? Intercept (αα) ? What is the standard error of the estimate (sese)? 1.754 1.532 105.182 What is the estimate of the standard deviation of the estimated slope (sbsb)? 1.897 0.028 0.032 Can you reject the hypothesis (at the 0.05 level of significance) that there is no relationship (i.e., β=0β=0) between the price and quantity variables? (Hint: t0.025,13=2.16t0.025,13=2.16) Yes No Complete the following worksheet and then use it to calculate the coefficient of determination. ii xixi yiyi yˆy^ (yˆi−y¯)2y^i−y¯2 (yi−y¯)2yi−y¯2 1 50 20 19.329 8.579 12.960 2 50 21 19.329 8.579 21.160 3 55 19 18.374 3.897 6.760 4 55 19.5 18.374 3.897 9.610 5 60 20.5 17.419 1.038 16.810 6 60 19 17.419 1.038 6.760 7 65 15.5 16.464 0.004 0.810 8 65 15 16.464 0.004 1.960 9 70 14.5 15.509 0.794 3.610 10 70 15.5 15.509 0.794 0.810 11 80 13 13.599 7.846 11.560 12 80 14 13.599 7.846 5.760 13 90 11.5 11.689 22.194 24.010 14 90 11 11.689 22.194 29.160 15 40 17 21.239 23.416 0.360 Total ? ? The coefficient of determination (r2r2) is? What is the price elasticity of demand at a price of 50 cents? -0.50 -0.46 -0.02 0.03

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter4: Estimating Demand

Section: Chapter Questions

Problem 2E

See similar textbooks

Related questions

Question

Complete the following worksheet and then estimate the demand function for Pilot's new pen using a linear regression model.

Test Market	Price Charged	Quantity Sold
(cents)	(Thousands of Pens)
ii	xixi	yiyi	xixiyiyi	xi2xi2	yi2yi2
1	50	20	1,000	2,500	400
2	50	21	1,050	2,500	441
3	55	19	1,045	3,025	361
4	55	19.5	1,072.5	3,025	380.25
5	60	20.5	1,230	3,600	420.25
6	60	19	1,140	3,600	361
7	65	15.5	1,007.5	4,225	240.25
8	65	15	975	4,225	225
9	70	14.5	1,015	4,900	210.25
10	70	15.5	1,085	4,900	240.25
11	80	13	1,040	6,400	169
12	80	14	1,120	6,400	196
13	90	11.5	1,035	8,100	132.25
14	90	11	990	8,100	121
15	40	17	680	1,600	289
Total	980	246	?	67,100	?

Regression Parameters	Estimations
Slope (ββ)	?
Intercept (αα)	?

What is the standard error of the estimate (sese)?

1.754

1.532

105.182

What is the estimate of the standard deviation of the estimated slope (sbsb)?

1.897

0.028

0.032

Can you reject the hypothesis (at the 0.05 level of significance) that there is no relationship (i.e., β=0β=0) between the price and quantity variables? (Hint: t0.025,13=2.16t0.025,13=2.16)

Yes

Complete the following worksheet and then use it to calculate the coefficient of determination.

ii	xixi	yiyi	yˆy^	(yˆi−y¯)2y^i−y¯2	(yi−y¯)2yi−y¯2
1	50	20	19.329	8.579	12.960
2	50	21	19.329	8.579	21.160
3	55	19	18.374	3.897	6.760
4	55	19.5	18.374	3.897	9.610
5	60	20.5	17.419	1.038	16.810
6	60	19	17.419	1.038	6.760
7	65	15.5	16.464	0.004	0.810
8	65	15	16.464	0.004	1.960
9	70	14.5	15.509	0.794	3.610
10	70	15.5	15.509	0.794	0.810
11	80	13	13.599	7.846	11.560
12	80	14	13.599	7.846	5.760
13	90	11.5	11.689	22.194	24.010
14	90	11	11.689	22.194	29.160
15	40	17	21.239	23.416	0.360
			Total	?	?

The coefficient of determination (r2r2) is?

What is the price elasticity of demand at a price of 50 cents?

-0.50

-0.46

-0.02

0.03

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.