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 i 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Total O 1.577 O 1.761 Regression Parameters Estimations Slope (B) Intercept (a) O 105.432 O 0.028 O 1.902 Price Charged (cents) Ii 50 50 55 55 60 60 65 65 70 70 80 O 0.032 What is the standard error of the estimate (se)? 80 90 90 40 Ο 980 Yes Quantity Sold (Thousands of Pens) No Yi 20 21 19 19.5 20.5 19 16.5 15 14 15.5 13 14 11.5 11 17 What is the estimate of the standard deviation of the estimated slope (st)? 246.5 Iiyi 1,000 1,050 1,045 1,072.5 1,230 1,140 1,072.5 975 980 1,085 1,040 1,120 1,035 990 680 1,² 2,500 2,500 3,025 3,025 3,600 3,600 4,225 4,225 4,900 4,900 6,400 6,400 8,100 8,100 1,600 67,100 2 Can you reject the hypothesis (at the 0.05 level of significance) that there is no relationship (i.e., B=0) between the price and quantity variables? (Hint: to.025,13 = 2.16) Yi 400 441 361 380.25 420.25 361 272.25 225 196 240.25 169 196 132.25 121 289
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 i 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Total O 1.577 O 1.761 Regression Parameters Estimations Slope (B) Intercept (a) O 105.432 O 0.028 O 1.902 Price Charged (cents) Ii 50 50 55 55 60 60 65 65 70 70 80 O 0.032 What is the standard error of the estimate (se)? 80 90 90 40 Ο 980 Yes Quantity Sold (Thousands of Pens) No Yi 20 21 19 19.5 20.5 19 16.5 15 14 15.5 13 14 11.5 11 17 What is the estimate of the standard deviation of the estimated slope (st)? 246.5 Iiyi 1,000 1,050 1,045 1,072.5 1,230 1,140 1,072.5 975 980 1,085 1,040 1,120 1,035 990 680 1,² 2,500 2,500 3,025 3,025 3,600 3,600 4,225 4,225 4,900 4,900 6,400 6,400 8,100 8,100 1,600 67,100 2 Can you reject the hypothesis (at the 0.05 level of significance) that there is no relationship (i.e., B=0) between the price and quantity variables? (Hint: to.025,13 = 2.16) Yi 400 441 361 380.25 420.25 361 272.25 225 196 240.25 169 196 132.25 121 289
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text: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
i
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Total
O 1.577
Regression Parameters Estimations
Slope (B)
Intercept (a)
O 1.761
O 105.432
O 0.028
Price Charged
(cents)
Xi
50
50
55
55
60
60
65
65
70
70
80
80
90
90
40
1.902
O 0.032
980
What is the standard error of the estimate (se)?
Quantity Sold
(Thousands of Pens)
O Yes
O No
Yi
20
21
19
19.5
20.5
19
16.5
15
14
15.5
13
14
11.5
11
17
What is the estimate of the standard deviation of the estimated slope (st)?
246.5
TiYi
1,000
1,050
1,045
1,072.5
1,230
1,140
1,072.5
975
980
1,085
1,040
1,120
1,035
990
680
I₂²
2,500
2,500
3,025
3,025
3,600
3,600
4,225
4,225
4,900
4,900
6,400
6,400
8,100
8,100
1,600
67,100
2
Can you reject the hypothesis (at the 0.05 level of significance) that there is no relationship (i.e., B = 0) between the price and quantity variables?
(Hint: to.025,13 = 2.16)
Y₁²
400
441
361
380.25
420.25
361
272.25
225
196
240.25
169
196
132.25
121
289
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