A consumer buying cooperative tested the effective heating area of 20 different
ID: 3157346 • Letter: A
Question
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 1,250 69 2 2,000 71 3 750 247 4 1,750 107 5 1,500 118 6 1,500 222 7 1,250 208 8 1,500 187 9 1,750 280 10 1,250 46 11 2,000 118 12 750 142 13 750 66 14 1,250 242 15 1,750 111 16 1,250 261 17 1,000 58 18 1,000 88 19 1,750 87 20 1,250 157 PictureClick here for the Excel Data File
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 0.010 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.)
a.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.)
Explanation / Answer
a) The correlation of Wattage and Area is 0.0317
The link (relationship) is Direct.
b) Test statistic value is t = -0.127
c) The regression equation is: Area = 155.005 - 0.006*Wattage.
d) heater 12 (750) looks like the best buy since this has the least residual
The summary of the regression output is as follows
SUMMARY OUTPUT Regression Statistics Multiple R 0.031748997 R Square 0.001007999 Adjusted R Square -0.061429001 Standard Error 81.07692619 Observations 18 ANOVA df SS MS F Significance F Regression 1 106.1237374 106.1237374 0.016144254 0.900476005 Residual 16 105175.4874 6573.467961 Total 17 105281.6111 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 155.0050505 67.931637 2.281779997 0.036529343 10.99641324 299.0136878 Wattage -0.006212121 0.048891226 -0.127060041 0.900476005 -0.10985689 0.097432648Related Questions
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