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Homework answers / question archive / You have been given data on Electricity usage

You have been given data on Electricity usage. You have data on the bill and a number of pieces of data thought to explain/predict the bill. I want you to **use the tools learned in this class** to tell me what I need to know in order to make a good explanation/prediction of electricity bills.

Using the data set “Electric Bill Data” and accompanying documentation in the ‘Class Project’ folder on the Jupiter site for the course, do the following:

1. Perform a multiple regression analysis **without** the Meter, Heating, Cooling dummy variables. Use the 5% level of significance.

2. Fully explain the results. This means discuss/interpret each term and its significance, explain what the coefficients mean, the R-square, and F-value.

3. Check for autocorrelation.

4. Check for multicollinearity. (Rule of thumb that a correlation of .7 or more is suspect).

(If not using Excel, construct a correlation matrix with coefficients and p values, if able to)

5. Add the three dummy variables. You must be careful, because it is possible to have any combination of new electric meter and new heating or cooling appliances. One can have none of these, one, two or all three, in various combinations. You should try to develop meaningful dummy variables such as:

1=None, 0=else;

1=all new, 0=else;

1=Emeter, 0=else;

1=Emeter and New Heat, 0=else;

1=New Heat, 0=else;

1=New Heat and New Cool, 0=else;

1=New Cool, 0=else.

6. Using the complete model, drop those variables that are not 5% significant.

7. Write out an ‘executive summary’ of your best results, as per the example below.

8. Using Bill and Time (why can’t you use year or month?), perform a simple regression, performing the analyses above. Forecast two months of bills ahead.

9. Using Bill and Time and Time^{2}, perform a simple regression, performing the analyses above. Forecast two months of bills ahead.

10. Of these last two models, which do you conclude is the best model? Why? Are either of these better than the multiple regressions performed above?

You may use Excel for the regression, or you may use another statistical package if you prefer.

*An example of the Executive Summary:*

*Write the equation, as you would in a business report: Give the full details in 2-7 above).*

*Y*

* = -07.755 - .23304X1 + .51618304X2 R² = .9653*

*(-.059) (26.166) Ra²= .962*

* F = 375.906*

*DW = 2.29*

*where **Y*

* = estimated quantity demanded of widgets per month*

*X1 = widget price, in dollars*

*X2 = U.S. disposable income, in thousands of dollars*

*If price rises by $1, the quantity demanded of widgets will fall by .233 widgets. *

*If Income rises by $1 thousand, the quantity demanded of widgets will rise by .516 widgets. *

*If Income were to rise by $1 million, the quantity demanded of widgets will rise by 516 widgets. *

*If (Dummy=1), then bill rises/falls by x, compared to (Dummy=0)*

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