Answered: A consumer buying cooperative tested…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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Question

A consumer buying cooperative tested the effective heating area of 20 different electric space heaters with different wattages. Here are the results.

Heater	Wattage	Area
1	750		291
2	1,750		83
3	1,250		215
4	1,750		209
5	1,500		295
6	750		153
7	1,000		40
8	750		166
9	1,250		115
10	1,250		146
11	750		113
12	1,000		56
13	1,750		284
14	1,000		45
15	750		82
16	1,250		175
17	750		150
18	1,500		231
19	1,000		87
20	750		52

Click here for the Excel Data File

Required:

a. Compute the correlation between the wattage and heating area. Is there a direct or an indirect relationship? (Round your answer to 4 decimal places.)

b. Conduct a test of hypothesis to determine if it is reasonable that the coefficient is greater than zero. Use the 0.050 significance level. (Round intermediate calculations and final answer to 3 decimal places.)

H₀: ρ ≤ 0; H₁: ρ > 0 Reject H₀ if t > 1.734

c. Develop the regression equation for effective heating based on wattage. (Negative value should be indicated by a minus sign. Round your answers to 3 decimal places.)

d. What heating area corresponds with a 1,500-watt heater? (Round your answers to 4 decimal places.)

e. What is the 95% confidence interval of heating the area if the wattage is 1,500? (Round your answers to 4 decimal places.)

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