Your interpretation of the coefficient of determination

MULTIVARIATE ESTIMATION AND MODEL FIT

 

Assignment Overview

 

You are a consultant who works for the Diligent Consulting Group. In this Case, you are engaged on a consulting basis by Loving Organic Foods. In order to get a better idea of what might have motivated customers’ buying habits you are asked to analyze the factors that impact organic food expenditures. You performed a simple linear regression analysis in the Module 3 Case. Now, you are adding a layer of complexity to that analysis and including more independent variables in your model.

 

Case Assignment

 

Using Excel, generate regression estimates for the following model:

 

Annual Amount Spent on Organic Food = α + b1Age + b2AnnualIncome

 

+ b3Number of People in Household + b4Gender

 

After you have reviewed the results from the estimation, write a report to your boss that interprets the results that you obtained. Please include the following in your report:

 

The regression output you generated in Excel.

 

Your interpretation of the coefficient of determination (r-squared).

 

Your interpretation of the global test for statistical significance (the F-test).

 

Your interpretation of the coefficient estimates for all the independent variables.

 

Your interpretation of the statistical significance of the coefficient estimates for all the independent variables.

 

The regression equation with estimates substituted into the equation. (Note: Once the estimates are substituted into the regression equation, it should take a form similar to this: y = 10 +2×1 +1×2 +4×3 +0.9×4)

 

An estimate of “Annual Amount Spent on Organic Food” for the average consumer. (Note: You will need to substitute the averages for all the independent variables into the regression equation for x, the intercept for α, and solve for y.)

 

A discussion of whether or not the coefficient estimate on the Age variable in this estimation is different than it was in the simple linear regression model from Module 3 Case. Be sure to explain why it did/did not change.

 

Data: Download the Excel-based data file: BUS520 Module 4 Case.

 

Assignment Expectations

 

Written Report

 

Length requirements: 3–4 pages minimum (not including Cover and Reference pages). Note: You must submit 3–4 pages of written discussion and analysis.

 

Provide a brief introduction to/background of the problem, similar to the introduction/background you provided in Module 1 through 3 Case submissions.

 

Provide a brief comparison of simple linear regression and multiple linear regression.

 

Provide a written analysis that addresses each of requirements listed under the “Case Assignment” section.

 

Write clearly, simply, and logically. Use double-spaced, black Verdana or Times Roman font in 12 pt. type size.

 

Please use keywords as headings to organize the report.

 

Avoid redundancy and general statements such as “All organizations exist to make a profit.” Make every sentence count.

 

Paraphrase the facts using your own words and ideas, employing quotes sparingly. Quotes, if absolutely necessary, should rarely exceed five words.

 

Upload both your written report and Excel file to the Case 4 Dropbox.

 

 

 

BUS520 Business Analytics and Decision Making

 

Module 4 SLP

 

MULTIVARIATE ESTIMATION AND MODEL FIT

 

Assume once again that you are a consultant who works for the Diligent Consulting Group. You are continuing to work on the analysis of the customer database from Modules 1 through 3.

 

SLP Assignment Expectations

 

Complete the following tasks in the Module 4 SLP assignment template:

 

Compare the coefficients of determination (r-squared values) from the two linear regressions: simple linear regression from Module 3 Case and the multivariate regression from Module 4 Case. Which model had the “best fit”?

 

Calculate the residual for the first observation from the simple linear regression model. Recall, the Residual = Observed value – Predicted value or e = y – ?.

 

What happens to the overall distance between the best fit line and the coordinates in the scatterplot when the residuals shrink?

 

What happens to the coefficient of determination when the residuals shrink?

 

Consider the r-squared from the linear regression model and the r-squared from the multivariate regression model. Why did the coefficient of determination change when more variables were added to the model?