Lecture 24 Multiple Regression Model And Residual Analysis BA 201 Lecture 24 Multiple Regression Model And Residual Analysis © 2001 Prentice-Hall, Inc.

Topics Developing the Multiple Linear Regression Residual Analysis © 2001 Prentice-Hall, Inc.

Simple and Multiple Regression Compared Coefficients in a simple regression pick up the impact of that variable plus the impacts of other variables that are correlated with it and the dependent variable but are excluded from the model. Coefficients in a multiple regression net out the impacts of other variables in the equation. Hence they are called the net regression coefficients. They still pick up the effects of other variables that excluded form the model but are correlated with the included variables and the dependent variable. © 2001 Prentice-Hall, Inc.

Simple and Multiple Regression Compared:Example Two simple regressions: Multiple Regression: © 2001 Prentice-Hall, Inc.

Simple and Multiple Regression Compared: Excel Output © 2001 Prentice-Hall, Inc.

Simple and Multiple Regression Compared: Excel Output © 2001 Prentice-Hall, Inc.

Venn Diagrams and Explanatory Power of a Simple Regression Variations in Oil explained by the error term Variations in Temp not used in explaining variation in Oil Oil Variations in Oil explained by Temp or variations in Temp used in explaining variation in Oil Temp © 2001 Prentice-Hall, Inc.

Venn Diagrams and Explanatory Power of a Simple Regression (continued) Oil Temp © 2001 Prentice-Hall, Inc.

Venn Diagrams and Explanatory Power of a Multiple Regression Variation NOT explained by Temp nor Insulation Overlapping variation in both Temp and Insulation are used in explaining the variation in Oil but NOT in the estimation of nor Oil Temp Insulation © 2001 Prentice-Hall, Inc.

Coefficient of Multiple Determination Proportion of Total Variation in Y Explained by All X Variables Taken Together Never Decreases When a New X Variable is Added to Model Disadvantage When Comparing Models © 2001 Prentice-Hall, Inc.

Venn Diagrams and Explanatory Power of Regression Oil Temp Insulation © 2001 Prentice-Hall, Inc.

Adjusted Coefficient of Multiple Determination Proportion of Variation in Y Explained by All X Variables adjusted for the Number of X Variables used Penalize Excessive Use of Independent Variables Smaller than Useful in Comparing among Models © 2001 Prentice-Hall, Inc.

Coefficient of Multiple Determination Excel Output Adjusted r2 reflects the number of explanatory variables and sample size is smaller than r2 © 2001 Prentice-Hall, Inc.

Interpretation of Coefficient of Multiple Determination 96.56% of the total variation in heating oil can be explained by different temperature and the variation in the amount of insulation 95.99% of the total fluctuation in heating oil can be explained by different temperature and the variation in the amount of insulation after adjusting for the number of explanatory variables and sample size © 2001 Prentice-Hall, Inc.

Using The Model to Make Predictions Predict the amount of heating oil used for a home if the average temperature is 300 and the insulation is 6 inches. The predicted heating oil used is 278.97 gallons © 2001 Prentice-Hall, Inc.

Predictions in PHStat PHStat | Regression | Multiple Regression … Check the “Confidence and Prediction Interval Estimate” box EXCEL spreadsheet for the heating oil example. © 2001 Prentice-Hall, Inc.

Another Example The Excel spreadsheet that contains the multiple regression result of regressing Mid-term scores on quiz scores and attendance score © 2001 Prentice-Hall, Inc.

Residual Plots Residuals Vs Residuals Vs Time May need to transform Y variable May need to transform variable May need to transform variable Residuals Vs Time May have autocorrelation © 2001 Prentice-Hall, Inc.

Residual Plots: Example Maybe some non-linear relationship No Discernable Pattern © 2001 Prentice-Hall, Inc.

Summary Discussed Residual Plots © 2001 Prentice-Hall, Inc.