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

1500

205

2

750

70

3

1500

199

4

1250

151

5

1250

181

6

1250

217

7

1000

94

8

2000

298

9

1000

135

10

1500

211

11

1250

116

12

500

72

13

500

82

14

1500

206

15

2000

245

16

1500

219

17

750

63

18

1,500

200

19

1250

151

20

500

44

a.Compute the correlation between the wattage and heating area. Is there a direct or an indirect relationship? (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

b. Conduct a test of hypothesis to determine if it is reasonable that the coefficient is greater than zero. Use the 0.01 significance level. (Negative value should be indicated by a minus sign. Round intermediate calculations and final answer to 3 decimal places.)

H0: 0; H1: > 0 Reject H0 if t > 1.7341

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 answer to 4 decimal places.)

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