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 43
2 1,250 138
3 1,250 103
4 1,000 142
5 1,500 95
6 750 162
7 1,000 51
8 2,000 163
9 2,000 284
10 2,000 230
11 1,250 134
12 1,000 228
13 1,000 41
14 750 126
15 1,750 286
16 750 102
17 1,750 144
18 750 132
19 1,750 111
20 2,000 196
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 0.010 significance level. (Round intermediate calculations and final answer to 3 decimal places.)
H0: Ļ ā¤ 0; H1: Ļ > 0
Reject H0 if t > 2.552
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.)
