A.     How many dummy variables does this regression use?

B.     What are the values of the dummy variables for urban, sub-urban, and rural? Assume rural is the base territory, with dummy variables equal to zero.

C.    Use Excel or other statistical software to run the regression. What are the values of á, â₁, and â₂? (Fox uses ã₁ and ã₂ instead of â₁ and â₂ for dummy variables.) Explain what each of the coefficients means.

 

Jacob: Fox uses both ã₁ and ã₂ as well as â₁ and â₂.

 

Rachel: We do this is the territory number has a quantitative value. But the territory numbers here are just indicators; they have no quantitative meaning. The regression equation is

 

Frequency = á + â₁ × D₁ + â₂ × D₂

 

In Fox’s notation, this is            Frequency = á + ã₁ × D₁ + ã₂ × D₂

 

 

In letter C and using Fox's notation Yi = α + βXi + γ1Di1 + γ2Di2, what will be the Xi here? Is it Xi = 1?

[NEAS: The posting is updated to clarify the notation.]

Can any one please tell me how to use excel to run regression.

[NEAS: Excel help says: “Use the Analysis ToolPak to perform complex data analysis: If you need to develop complex statistical or engineering analyses, you can save steps and time by using the Analysis ToolPak. You provide the data and parameters for each analysis, and the tool uses the appropriate statistical or engineering macro functions to calculate and display the results in an output table. Some tools generate charts in addition to output tables. To use the Analysis ToolPak, click Data Analysis in the Analysis group on the Data tab. If the Data Analysis command is not available, you need to load the Analysis ToolPak add-in program.” The Analysis TookPak is explained (somewhat) in the on-line help facility. The exhibits and graphics produced are the same as those in the Fox textbook.]

NEAS, thanks for adding the additional explanation. Unfortunately, I'm having trouble understanding Rachel's answer. There appears to be a grammatical error in the first sentence, but I cannot figure out what it is supposed to say. Could you please correct this?

See the PDF that NEAS posted on the Module 14 HW thread. I'd suggest googling "regression in excel." Also, I'm finding _Statistics with Microsoft Excel_ by Beverly J. Dretzke very helpful.

Rachel: We do this is the territory number has a quantitative value.

 

I believe this is intended to say "We would do this if the territory numbers had quantitative value."

Is the answer for C supposed to be in the format:
Y Hat = a + bX +G1D1+G2D2?

Do we just do an excel regression with 3 variables (territory, D1 and D2)?

I did an excel regression with 2 variables: D1, D2.  I didn't treat territory as an explanatory variable but rather as a category (like the occupational types on page 125).

I came up with

Y = A + B₁D₁ + B₂D₂ = .0954 + .0564*D₁ + .0296 * D₂

Did anyone come up with anything similar to this?

Got exactly those numbers.

For Excel 2010, here are instructions for loading the analysis toolpak:

The Analysis ToolPak is a Microsoft Excel add-in (add-in: A supplemental program that adds custom commands or custom features to Microsoft Office.) program that is available when you install Microsoft Office or Excel. To use it in Excel, however, you need to load it first.

1. Click the File tab, and then click Options.
2. Click Add-Ins, and then in the Manage box, select Excel Add-ins.
3. Click Go.
4. In the Add-Ins available box, select the Analysis ToolPak check box, and then click OK.
   1. Tip    If Analysis ToolPak is not listed in the Add-Ins available box, click Browse to locate it.
   2. If you get prompted that the Analysis ToolPak is not currently installed on your computer, click Yes to install it.
5. After you load the Analysis ToolPak, the Data Analysis command is available in the Analysis group on the Data tab.

 Note   To include Visual Basic for Application (VBA) functions for the Analysis ToolPak, you load the Analysis ToolPak - VBA add-in the same way that you load the Analysis ToolPak. In the Add-ins available box, select the Analysis ToolPak - VBA check box, and then click OK.

Once the analysis toolpak is loaded, click on Data Analysis in the Analysis group and then on Regression. The screen that comes up asks for the cells with X-values and Y-values and the cells in which the ouput should be placed.