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 1,000 108 2 750 291 3 1,500 100 4 1,000 43 5 1,250 68 6 1,500 181 7 1,250 254 8 750 228 9 1,500 126 10 1,500 166 11 750 45 12 750 237 13 1,000 75 14 1,750 126 15 1,750 249 16 1,750 105 17 1,750 298 18 1,250 212 19 750 98 20 750 185 Click here for the Excel Data File 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.)
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 | 1,000 | 108 | ||
| 2 | 750 | 291 | ||
| 3 | 1,500 | 100 | ||
| 4 | 1,000 | 43 | ||
| 5 | 1,250 | 68 | ||
| 6 | 1,500 | 181 | ||
| 7 | 1,250 | 254 | ||
| 8 | 750 | 228 | ||
| 9 | 1,500 | 126 | ||
| 10 | 1,500 | 166 | ||
| 11 | 750 | 45 | ||
| 12 | 750 | 237 | ||
| 13 | 1,000 | 75 | ||
| 14 | 1,750 | 126 | ||
| 15 | 1,750 | 249 | ||
| 16 | 1,750 | 105 | ||
| 17 | 1,750 | 298 | ||
| 18 | 1,250 | 212 | ||
| 19 | 750 | 98 | ||
| 20 | 750 | 185 | ||
Click here for the Excel Data File
a. Compute the
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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