Inverse regression 2

Download: InverseRegression2_init.xlsx

Introduction

In this screencast we will perform inverse regression using polynomial regression models. The CLS-Stats add-in provides some tools for this task and we will explore them here as well as how to recognize edge cases in inverse regression.

Learning Goals

• Review and additional practice at choosing appropriate polynomial regression models
• Learn to use the PolyInv function and the Inverse Regression VBA procedure (which invokes SOLVER). You should consider reviewing the documentation for both of these:
  • PolyInv lambda function
  • Inverse Regression VBA procedure
• Learn to recognize when edge cases might occur and what causes them

Tasks

• Use PolyPred to add the best fit ($\hat{y}$) and the prediction band to the plot. It should respond to changes in the order.
• Use residuals (plots and statistics) to choose an appropriate order for the polynomial fit
• Use PolyInv to calculate the (approximate) confidence intervals for $x_u$ for each of the two $y_u$ values
• Use the Inverse Regression VBA procedure to calculate exact CIs for those values and explain any descrepancies

At the end of your screencast your spreadsheet should look something like the image below.