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Multiple Regression: Analyzing Predictor Variables and Assessing Significance

In this .Stat.324. course, we will explore multiple regression analysis techniques, including matrix scatterplots, correlation matrices, and F-tests. We will examine how each predictor variable is related to the response variable and assess the need for transformations. Additionally, we will evaluate unusual observations and analyze how predictors are related to each other. Furthermore, we will interpret slopes conditional on other variables and determine which variable is most strongly related to unexplained variation. Finally, we will discuss the significance of additional explanatory ability and the importance of considering all variables in the model.

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Multiple Regression: Analyzing Predictor Variables and Assessing Significance

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  1. Stat 324 – Day 17 Multiple Regression F-tests

  2. Last Time – Multiple Regression • Matrix scatterplot • Correlation matrix • How is each predictor related to response? • Need transformations? Unusual observations? • How are predictors related to each other? • Least Squares equation • Interpreting slopes conditional on other variables in model

  3. Added Variable and Leverage Plots • Which variable is more strongly related to the unexplained variation in acceleration after accounting for horsepower?

  4. Sums of squares • Adjusted vs. Sequential Sums of Squares • Look at reduction in SSE with new variable either • With all other variables in model • With the previously listed variables in model • Help assess significance of “additional” explanatory ability of new variable • Variables that are related to response may not be useful after adjusting for other variables

  5. F tests • These tests also reflect (all) other variables in the model

  6. Sequential tests • These tests reflect only the “previous” variables in the model H0: btuition = 0 H0: b%facPhD = 0 with btuition≠ 0 H0: bSF ratio = 0 with b%facPhD, btuition≠ 0

  7. F tests • These tests also reflect (all) other variables in the model H0: btuition = 0 with b%facPhD, bSFratio≠ 0

  8. Don’t forget residuals!

  9. And case influence statistics

  10. JMP output

  11. Exam 1 • Things to watch for: • Parameter vs. Statistic • F-statistics need two df values • “It will be better” • “The SD will be smaller”

  12. To Do • HW 4 • PP • Probably won’t have 10-11 office hour tomorrow

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