Question

1. You are interested in lowering the consumption of electricity (Kwh) in your firm. You have data on the mean ambient temperature (MeanTemp), No. of days that heat was generated (HeatingDays), No. of days that the air conditioner was switched on (CoolingDays), New construction (1- Yes, 0 – No) (NewRoom), and the two different ways that the electric meter was read (Method) (0- Estimate 1- Actual). Here is the regression result.

Predictor      Coef SE Coef      T      P

Constant      635.0    230.0   2.76 0.007

MeanTemp     -3.604    3.544 -1.02 0.312

HeatingDays 0.0173   0.1238   0.14 0.889

CoolingDays 0.1118   0.2386   0.47 0.641

NewRoom      179.05    33.07   5.41 0.000

Method       -30.61    27.56 -1.11 0.270

S = 122.684   R-Sq = 40.1%   R-Sq(adj) = 36.1%

Analysis of Variance

Source          DF       SS      MS      F      P

Regression       5   754529 150906 10.03 0.000

Residual Error 75 1128847   15051

Total           80 1883376

1. State your alternate hypotheses between Kwh and (3 points)

1. Mean Temp

      

       2.New Room

         3.Have your hypotheses been supported?

      4.What is the trend line (regression line)?

       5.Have you accounted for 100% of the factors that can explain electricity consumption? How can you tell?

Answer 1

(a)

H_A: Coefficient of MeanTemp is not equal to zero

(b)

H_A: Coefficient of NewRoom is not equal to zero

(c)

The P value for the coefficient of MeanTemp is 0.312 which is more than the alpha=0.05. So, at 95% confidence level, the null hypothesis that the coefficient is zero is supported and hence the alternative hypothesis is not supported.

The P value for the coefficient of NewRoom is 0.000 which is less than the alpha=0.05. So, at 95% confidence level, the null hypothesis that the coefficient is zero is rejected and hence the alternative hypothesis is supported.

(d)

Regression Line:

Kwh = 635 - 3.604 * MeanTemp + 0.0173 * HeatingDays + 0.1118 * Cooling Days + 179.05 * NewRoom - 30.61 * Method

If we go by the statistical significance of the coefficient and the intercepts, the coefficient of NewRoom is only significant at 95% confidence level. So, the regression equation may also be reduced to:

Kwh = 179.05 * NewRoom

(e)

The R-squared value is only 40% which indicates that only 40% of the variation of the data is explained by the predictors. So, more variables may be required in order to explain the variation.