Multivariate Estimation and Model Fit

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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:

  1. Compare the coefficients of determination (r-squared values) from the three linear regressions: simple linear regression from Module 3 Case, multivariate regression from Module 4 Case, and the second multivariate regression with the logged values from Module 4 Case. Which model had the “best fit”?
  2. Calculate the residual for the first observation from the simple linear regression model. Recall, the Residual = Observed value – Predicted value or e = y – ŷ.
  3. What happens to the overall distance between the best fit line and the coordinates in the scatterplot when the residuals shrink?
  4. What happens to the coefficient of determination when the residuals shrink?
  5. Consider the r-squared from the linear regression model and the r-squared from the first multivariate regression model. Why did the coefficient of determination change when more variables were added to the model?

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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