Gm533 Week 7 Discussion

A homeowner recorded the amount of electricity in kilowatt-hours (KWH) consumed in his house on each of 21 days. He also recorded the numbers of hours his air conditioner (AC) was turned on and the numbers of times his electric clothes dryer (DRYER) was operated. His objective was to relate the KWH consumption to the AC and DRYER usage. In addition, he wanted to know how many KWH’s the AC used per hour and the number of KWH’s used in each run of the DRYER. Statistical regression analysis can serve this purpose. Use chapter 14 as a guideline to develop a regression model that predicts KWH consumption from AC and Dryer usage.
1. Perform a simple linear regression using only AC to predict KWH.
2. Perform a simple linear regression using only Dryer to predict KWH.
3. Perform a multiple linear regression using both AC and Dryer to predict KWH.
4. Compare pvalues for the F-test, Rsquare, and the regression coeficients for the results of 1, 2, and 3. To maximize participation (and credit), do task 1 and 2 on one day, 3 on the second day, and 4 on the third day for a total of three posts.
Question 1
Regression Analysis: KWH versus AC
The regression equation is KWH = 27.9 + 5.34 AC

Predictor Coef SE Coef T P
Constant 27.851 7.807 3.57 0.002
AC 5.341 1.031 5.18 0.000

S = 14.4530 R-Sq = 58.6% R-Sq(adj) = 56.4%

Analysis of Variance
Source DF SS MS F P
Regression 1 5609.7 5609.7 26.85 0.000
Residual Error 19 3968.9 208.9
Total 20 9578.6

Question 2
Regression Analysis: Dryer versus KWH
The regression equation is Dryer = - 0.395 + 0.0281 KWH

Predictor Coef SE Coef T P
Constant -0.3948 0.5897 -0.67 0.511
KWH 0.028113 0.008636 3.26 0.004

S = 0.845182 R-Sq = 35.8% R-Sq(adj) = 32.4%

Analysis of Variance

Source DF SS MS F P
Regression 1 7.5705 7.5705 10.60 0.004