Multivariate estimation and model fit

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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.
You decide you want to generate an elasticity coefficient, so you log the following variables in Excel: Annual Amount Spent on Organic Food, Annual Income.
Using Excel, generate regression estimates for the following model:

Log(Annual Amount Spent on Organic Food) = α +b1Age + b2Log(AnnualIncome)
+ b3Number of People in Household + b4Gender

Your interpretation of the coefficient estimate for Log(AnnualIncome).
Your interpretation of the coefficient of determination (r-squared) for this new model.

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.

REQUIRED READING

The primary resource for this module is Introductory Business Statistics, by Alexander, Illowsky, and Dean.

Alexander, H., Illowsky, B., & Dean, S. (2017). Introductory Business Statistics. Openstax. Retrieved from https://openstax.org/details/books/introductory-business-statistics

For Module 3, you should read through the following material in this textbook.

Chapter 13: Linear Regression and Correlation
Sections 13.4, 13.5, and 13.6 only
These sections introduce multivariate or multiple linear regression analysis. These sections also explain some of the problems that can occur in regression analysis as well as how to change the functional form of the model to generate elasticity coefficients.

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