1. Lecture 24 Multiple Regression Model And Residual Analysis
BA 201
Lecture 24
Multiple Regression Model
And
Residual Analysis
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2. Topics Developing the Multiple Linear Regression Residual Analysis
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3. 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.
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4. Simple and Multiple Regression Compared:Example
Two simple regressions:
Multiple Regression:
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5. Simple and Multiple Regression Compared: Excel Output
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6. Simple and Multiple Regression Compared: Excel Output
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7. 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
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8. Venn Diagrams and Explanatory Power of a Simple Regression
(continued)
Oil
Temp
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9. 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
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10. 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
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11. Venn Diagrams and Explanatory Power of Regression
Oil
Temp
Insulation
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12. 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
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13. Coefficient of Multiple Determination
Excel Output
Adjusted r2
reflects the number of explanatory variables and sample size
is smaller than r2
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14. 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
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15. 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 gallons
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16. Predictions in PHStat PHStat | Regression | Multiple Regression …
Check the “Confidence and Prediction Interval Estimate” box
EXCEL spreadsheet for the heating oil example.
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17. Another Example
The Excel spreadsheet that contains the multiple regression result of regressing Mid-term scores on quiz scores and attendance score
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18. 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
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19. Residual Plots: Example
Maybe some non-linear relationship
No Discernable Pattern
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20. Summary
Discussed Residual Plots
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