A consumer buying cooperative tested the effective heating area of 20 different

Question

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

Compute the correlation between the wattage and heating area. Is there a direct or an indirect relationship? (Negative values 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 0.100 significance level. (Negative values should be indicated by a minus sign. Round your answer to 3 decimal places.)

Develop the regression equation for effective heating based on wattage. (Negative values 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 2 decimal places.)

  The sixth heater is the "best buy." It heats an area that is ? square feet
larger than estimated by the regression equation.

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

Explanation / Answer

a) correlation coefficient r=Sxy/(sxx*syy)1/2 =-0.2499

b)here test stat t=r*((n-2)/(1-r2))1/2=-1.095

c) from above b1=Sxy/Sxx=-0.0695

and Bo=Ybar-b1*Xbar =250.75

hence regression equation Area =250.75-0.0695*Wattage

d)173.25 feet larger

x Y (X-Xbar)^2 (Y-Ybar)^2 (X-Xbar)(Y-Ybar) Yi'=b0+x*b1 (Y-Yi')^2 (Ybar-Yi')^2 1500 74 10000.0000 6312.303 -7945.000 146.5000 5256.2500 48.30 1000 237 160000.0000 6980.603 -33420.000 181.2500 3108.0625 772.84 1500 50 10000.0000 10701.903 -10345.000 146.5000 9312.2500 48.30 1500 133 10000.0000 418.203 -2045.000 146.5000 182.2500 48.30 1500 89 10000.0000 4153.803 -6445.000 146.5000 3306.2500 48.30 2000 285 360000.0000 17305.403 78930.000 111.7500 30015.5625 1738.89 1500 251 10000.0000 9516.003 9755.000 146.5000 10920.2500 48.30 1250 291 22500.0000 18920.003 -20632.500 163.8750 16160.7656 108.68 1000 121 160000.0000 1053.003 12980.000 181.2500 3630.0625 772.84 1750 148 122500.0000 29.702 -1907.500 129.1250 356.2656 591.71 1750 111 122500.0000 1802.003 -14857.500 129.1250 328.5156 591.71 1000 254 160000.0000 10110.303 -40220.000 181.2500 5292.5625 772.84 1750 103 122500.0000 2545.203 -17657.500 129.1250 682.5156 591.71 1000 299 160000.0000 21184.803 -58220.000 181.2500 13865.0625 772.84 1250 115 22500.0000 1478.403 5767.500 163.8750 2388.7656 108.68 1000 200 160000.0000 2166.903 -18620.000 181.2500 351.5625 772.84 1750 106 122500.0000 2251.503 -16607.500 129.1250 534.7656 591.71 1250 74 22500.0000 6312.303 11917.500 163.8750 8077.5156 108.68 1500 64 10000.0000 8001.303 -8945.000 146.5000 6806.2500 48.30 1250 64 22500.0000 8001.303 13417.500 163.8750 9975.0156 108.68 28000.0000 3069.0000 1800000.0000 139244.9500 -125100.000 130550.5 8694.45 1400.000 153.45 Sxx Syy Sxy

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