Regression assignment | Mathematics homework help

Regression Assignment
OG&E Residential Sales

Point Value:  100 points         Due Date and Time:  See Syllabus/Schedule

Total Grade: Your total grade will be broken into 3 parts, 40 pts. for the initial analysis, 10 pts. for class discussion, and 50 pts. for the final analysis.  (See extra points below)

Extra points:  An additional 25 points may be added for superior analysis and demonstrated understanding.

Assignment:  Three parts to this assignment.

Preliminary Instructions:  Read through Parts 1, 2 and 3.  For each part, you should submit 2 subparts: a) your equations; b) your explanation.  I find it more convenient to submit explanations in a Word document, but you may do it as part of your Excel document. 

In your explanation you should focus on the following:

·         Statistical reasons and logic for why you selected the independent variables you selected.

·         The correlations between the dependent variable and the independent variables.

·         The correlation between independent variables.

·         What inferences do you gain by looking at the coefficients of the independent variables.

·         Explain the meaning of the independent variables t-statistics.

·         How do the adjusted r² and the standard error of the equation impact your selection of a good equation?

Part 1 is to develop an equation that best models the relationship between the independent variable, Y, and one or more of the dependent variables, X₁, X₂, X₃,…, X_n, using multiple linear regression techniques.  The monthly data found in the MS Excel file named Regression Assignment – Data Ch13&14 is to be used in your assignment.  The dependent variable, Y, is OK Residential MWH, described in number 1, below, and the potential independent variables, X₁, X₂, X₃,…,X_n, are described as numbers 2 through 11, below.  Be sure to explain why you included the independent variables that you included, and why you excluded other potential independent variables.  Address the following questions when you look at the independent variable:  Will this independent variable help determine future quantities of electricity purchases?  Does this independent variable help explain the reason residential customers use more or less electricity?  [Hint:  Not all the provided independent variables should be used in the final equation. You must determine which independent variables model the dependent variable the best.  You should eliminate independent variables that cause multicollinearity (see page 465 & 466). ]

Part 1:Post your results in Dropbox in the Online Classroom. 

Part 2:  You must describe the process and logic used for selecting the particular independent variables that you selected for your final equation.  In your description, you must explain the process of testing different independent variables and the results of various tests, plus describe the summary statistics that helped you select the best independent variables.  Be sure to explain why you excluded some of the potential independent variables.   

Part 2: Must be posted in the Discussion Forum and in the Dropbox.

Part 3:  Based upon input from other class members refine your regression model and your explanation.  Included in your final submitted files, Excel and Word files, should be all the requirements of Part 1 and Part 2, plus any improvements you make after reviewing Part 2 of other students.   Further, you must develop a forecast of the monthly KWH sales for the year 2012, using the data in MWH Regression Data in lines 219 -230.

Part 3:Post your results in Dropbox in the Online Classroom. 

Description of Independent and Dependent Variables:

In the MS Excel file named Special Regression Assignment Data – Chap13-14, you will find the following data series with the labels as follows:

1.            OK Residential MWH – Oklahoma residential sales of electricity in thousands of KWH (1000 KWH = Megawatt Hours- MWH).

2.            OK Residential Electric Price ($/KWH) – average Oklahoma Residential Electric Price (Dollars per KWH) for each month.  Special Instructions: You will include this independent variable regardless of the correlations you find or the t-stat.

3.            OK Real Personal Income (2000 $Mil) – Oklahoma Real Personal Income in millions of constant 2000 dollars.  Personal income is the income earned by persons in the state.  It does not include income earned by businesses.

4.            OK Real Personal Income Ex-Energy (2000 $Mil) – Oklahoma Real Income less the personal income earned by persons in the energy sector.

5.            OK Real Non-Farm Real Personal Income ($ Mil 2000) – Oklahoma real personal income excluding income earned by farming proprietors in 2000 dollars.

6.            OK Total Spending ($ Mil 2000) – Oklahoma monthly real total spending on all consumer goods in millions of constant 2000 dollars.

7.            OK Real GSP (2000 $Mil) – Oklahoma real gross state product (GSP) in millions of constant 2000 dollars.  GSP is a measure of output of goods and services in the state.  Output is closely tied to total income.

8.            OK Real GSP Ex-Energy (2000 $Mil) – Oklahoma real GSP less the output of the energy sector.

9.            Oklahoma Population (Thou) – Monthly Oklahoma population in thousands.

10.        Oklahoma Non-Farm Population (Thou) – Monthly non-rural Oklahoma population in thousands.

11.        OK Winter HDD – Oklahoma heating degree days – this is a numerical value representing hours in the month where heating is required.  The larger the number the more a residential customer might demand heat.

12.        OK Summer CDD – Oklahoma cooling degree days – this is a numerical value representing hours in the month where cooling is required.  The larger the number the more a residential customer might demand use of their air conditioners.