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 1560 175 2 720 85 3 1450 216 4 1290 173 5 1180 188 6 1340 236 7 920 85 8 1920 301 9 1020 164 10 1490 240 11 1170 131 12 410 48 13 530 56 14 1570 231 15 1940 260 16 1440 238 17 650 72 18 1420 196 19 1190 147 20 460 31 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.) Conduct a test of hypothesis to determine if it is reasonable that the coefficient is greater than zero. Use the 0.05 significance level. (Negative value should be indicated by a minus sign. Round intermediate calculations and final answer to 3 decimal places.) H0: ρ ≤ 0; H1: ρ > 0 Reject H0 if t > 1.7341 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.) Which heater looks like the "best buy" based on the size of the residual? (Negative value should be indicated by a minus sign. Round residual value to 2 decimal places.)
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To compute the correlation coefficient, we need to find the mean of wattage (X), the mean of heating area (Y), the standard deviation of wattage (sX), the standard deviation of heating area (sY), and the covariance between wattage and heating area (covXY). Mean Show more…
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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 1,750 455 2 1,500 35 3 2,200 565 4 2,100 455 5 1,750 255 6 1,300 55 7 1,400 335 8 1,000 35 9 2,300 555 10 1,250 35 11 2,000 545 12 1,400 125 13 1,200 45 14 1,250 135 15 2,300 555 16 2,300 565 17 2,800 655 18 1,000 35 19 800 45 20 300 20 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.) 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: ρ ≤ 0; H1: ρ > 0 Reject H0 if t > 2.5524 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.)
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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 1 750 125 2 1,000 145 3 1,750 204 4 2,000 132 5 1,500 108 6 1,000 51 7 1,250 232 8 750 128 9 2,000 297 10 1,250 271 11 1,500 41 12 1,750 275 13 2,000 285 14 2,000 259 15 1,500 156 16 1,250 252 17 750 61 18 750 72 19 1,500 41 20 1,250 164 Compute the correlation between the wattage and heating area. Is there a direct or an indirect relationship? (Round your answer to 4 decimal places.) Conduct a test of hypothesis to determine if it is reasonable that the coefficient is greater than zero. Use the 0.025 significance level. (Round intermediate calculations and final answer to 3 decimal places.) H0: ρ ≤ 0; H1: ρ > 0 Reject H0 if t > 2.101 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.) Which heater looks like the “best buy” based on the size of the residual? (Round residual value to 3 decimal places.)
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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 1,500 131 2 1,500 142 3 750 111 4 1,500 264 5 1,250 237 6 1,750 267 7 1,500 61 8 2,000 135 9 2,000 263 10 2,000 263 11 750 125 12 1,500 76 13 2,000 77 14 750 170 15 1,000 165 16 1,000 152 17 1,000 238 18 1,750 209 19 1,250 167 20 1,750 75 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: ρ ≤ 0; H1: ρ > 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.)
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