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Topic 13: Multiple Linear Regression Example

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    1. Topic 13: Multiple Linear Regression Example

    3. Study of CS students Computer science majors at Purdue have a large drop out rate Can we find predictors of success Predictors must be available at time of entry into program

    4. Data available GPA after three semesters High school math grades High school science grades High school English grades SAT Math SAT Verbal Gender (of interest for other reasons)

    5. Data for CS Example Y is grade point average 3 HS grades and 2 SATs are the explanatory variables (p=6) Have n=224 students

    6. Descriptive Statistics

    7. Output from Proc Means

    8. Output from Proc Means

    9. Descriptive Statistics

    11. High School Math

    12. High School Science

    13. High School English

    14. SAT Math

    15. SAT Verbal

    16. Interactive Data Analysis Click on menu Solutions -> analysis -> interactive data analysis Obtain SAS/Insight window Open library work Click on Data Set A1 (if it exists) Open

    17. Scatter Plot Matrix (shift) Click on GPA, SATM, SATV Go to menu Analyze Choose option Scatterplot(XY) Try some other options

    18. Scatter Plot Matrix

    19. Correlations

    20. Output from Proc Corr

    21. Output from Proc Corr

    22. Output from Proc Corr

    23. Use High School Grades to predict GPA

    25. CS ANOVA Table

    26. Remove HSS

    28. Rerun with HSM only

    30. SATs

    32. HS and SATs

    36. Best Model?

    37. Key ideas from case study First, look at graphical and numerical summaries for one variable at a time Then, look at relationships between pairs of variables with graphical and numerical summaries. Use plots and correlations

    38. Key ideas from case study The relationship between a response variable and an explanatory variable depends on what other explanatory variables are in the model A variable can be a significant (P<.05) predictor alone and not significant (P>0.5) when other Xs are in the model

    39. Key ideas from case study Regression coefficients, standard errors and the results of significance tests depend on what other explanatory variables are in the model

    40. Key ideas from case study Significance tests (P values) do not tell the whole story Squared multiple correlations give the proportion of variation in the response variable explained by the explanatory variables) can give a different view We often express R2 as a percent

    41. Key ideas from case study You can fully understand the theory in terms of Y = X + ? To effectively use this methodology in practice you need to understand how the data were collected, the nature of the variables, and how they relate to each other

    42. Background Reading