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Partial Regression Plots

Partial Regression Plots. Life Insurance Example: (nknw364.sas). Y = the amount of life insurance for the 18 managers (in $1000) X 1 = average annual income (in $1000) X 2 = risk aversion score (0 – 10). Life Insurance: Input, diagnostics. title1 h = 3 'Insurance' ; data insurance;

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Partial Regression Plots

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  1. Partial Regression Plots

  2. Life Insurance Example: (nknw364.sas) Y = the amount of life insurance for the 18 managers (in $1000) X1 = average annual income (in $1000) X2 = risk aversion score (0 – 10)

  3. Life Insurance: Input, diagnostics title1h=3'Insurance'; data insurance; infile'I:\My Documents\Stat 512\CH10TA01.DAT'; input income risk amount; run; procprintdata=insurance; run; *diagnostics; title2h=2'residual plots'; symbol1v=circle c=black; procregdata=insurance; model amount = income risk/rp; plotr.*(p. income risk); run;

  4. Life Insurance: output, diagnostics

  5. Life Insurance: Initial Regression

  6. Life Insurance: Scatter plot title2h=2'Scatterplot'; procsgscatterdata=insurance; matrix income risk amount; run;

  7. Life Insurance – Residual Plots

  8. Life Insurance – Residual Plots (cont)

  9. Life Insurance: Partial Regression Plots (1) procregdata=insurance; model amount=income risk/partial; run;

  10. Life Insurance: Partial Regression Plots (1)

  11. Life Insurance: Partial Regression Plots (2)risk title1h=3'Partial residual plot'; title2h=2'for risk'; symbol1v=circle i=rl; axis1label=(h=2'Risk Aversion Score'); axis2label=(h=2angle=90'Amount of Insurance'); procregdata=insurance; model amount risk = income; outputout=partialriskr=resamtresrisk; procgplotdata=partialrisk; plotresamt*resrisk / haxis=axis1 vaxis=axis2 vref = 0; run;

  12. Life Insurance: Partial Regression Plots (2)risk (cont)

  13. Life Insurance: Partial Regression Plots (2)income axis3label=(h=2'Income'); title2h=2'for income'; procregdata=insurance; model amount income = risk; outputout=partialincomer=resamtresinc; procgplotdata=partialincome; plotresamt*resinc / haxis=axis3 vaxis=axis2 vref = 0; run;

  14. Life Insurance: Partial Regression Plots (2)income (cont)

  15. Life Insurance: Quadratic title1'Quadratic model'; title2''; data quad; set insurance; sinc = income; procstandarddata=quad out=quad mean=0; varsinc; data quad; set quad; incomesq = sinc*sinc; proccorrdata=quad; var amount risk income incomesq; run; procregdata=quad; model amount = income risk incomesq; run;

  16. Life Insurance: Quadratic (regression)

  17. Life Insurance: Quadratic (residual plots)

  18. Life Insurance: normality Original Model With Quadratic Term

  19. Types of Outliers

  20. Life Insurance: Studentized Residuals (nknw364.sas) procregdata=quad; model amount=income risk incomesq/r; outputout = diagr=residstudent=student; run; procprintdata=diag; run;

  21. Life Insurance: Studentized Residuals (cont)

  22. Life Insurance: Studentized Residuals (cont)

  23. Life Insurance: Studentized Deleted Residuals procregdata=quad; model amount=income risk incomesq/rinfluence; outputout = diag1 r=residrstudent=rstudent; run; procprintdata=diag1; run;

  24. Studentized Deleted Residuals (cont)

  25. Studentized Deleted Residuals (cont)

  26. Studentized Deleted Residuals (cont)

  27. Studentized Deleted Residuals: w/o square

  28. /r vs. /influence • /r keyword • /influence keyword

  29. Hat Matrix Diagnosis, DFFITS

  30. Cook’s Distance, DFBetas, Cov Ratio

  31. Life Insurance: Multicollinearity procregdata=quad; model amount=income risk incomesq/tolvif; run;

  32. Body Fat: Multicollinearity (nknw260b.sas) databodyfat; infile'I:\My Documents\Stat 512\CH07TA01.DAT'; inputskinfold thigh midarm fat; procprintdata=bodyfat; run; procregdata=bodyfat; model fat=skinfold thigh midarm/viftol; run;

  33. Blood Pressure Example: Background (nknw406.sas) Researching the relationship between blood pressure in healthy women ages 20 – 60. Y = diastolic blood pressure (diast) X = age n = 54

  34. Blood Pressure: input data pressure; infile‘H:\My Documents\Stat 512\CH11TA01.DAT'; input age diast; procprintdata=pressure; run; title1h=3'Blood Pressure'; title2h=2'Scatter plot'; symbol1v=circle i=sm70 c=purple; axis1label=(h=2); axis2label=(h=2angle=90); procsortdata=pressure; by age; procgplotdata=pressure; plotdiast*age; run;

  35. Blood Pressure: Scatterplot

  36. Blood Pressure: regression (unweighted) procregdata=pressure; modeldiast=age / clb; outputout=diagr=resid; run;

  37. Blood Pressure: Residual Plots datadiag; setdiag; absr=abs(resid); sqrr=resid*resid; title2h=2'residual abs(resid) squared residual plots vs. age'; procgplotdata=diag; plot (residabsrsqrr)*age/haxis=axis1 vaxis=axis2; run;

  38. Blood Pressure: Residual Plots (cont)

  39. Blood Pressure: computing weights procregdata=diag; modelabsr=age; outputout=findweightsp=shat; datafindweights; setfindweights; wt=1/(shat*shat);

  40. Blood Pressure: computing weights if using resid2 proc reg data=diag; model sqrr=age; output out=findweights p=shat2; data findweights; set findweights; wt=1/shat2;

  41. Blood Pressure: weighted regression procregdata=findweights; modeldiast=age / clbp; weight wt; outputout = weighted r = residp = predict; run;

  42. Blood pressure: Comparison • Normal Regression • Weighted Regression

  43. Blood Pressure: new residuals datagraphtest; set weighted; resid1 = sqrt(wt)*resid; title2h=2'Weighted data - residual plot'; symbol1v=circle i=nonecolor=red; procgplotdata=graphtest; plot resid1*predict/vref=0haxis=axis1 vaxis=axis2; run;

  44. Blood Pressure: new residuals

  45. Biased vs. Unbiased Estimators

  46. Body Fat Example (ridge.sas) n = 20 healthy female subjects ages of 25 – 34 Y = body fat (fat) X1 = triceps skinfoldthickness (skinfold) X2 = thigh circumference (thigh) X3 = midarmcircumference (midarm) Previous Conclusion: Problem with multicollinearity Good model with a) thigh only or with b) midarm and skinfold only

  47. Body Fat Example: Regression (input) databodyfat; infile'I:\My Documents\Stat 512\CH07TA01.DAT'; inputskinfold thigh midarm fat; procprintdata=bodyfat; run; procregdata=bodyfat; model fat=skinfold thigh midarm; run;

  48. Body Fat Example: Regression (output)

  49. Body Fat Example: Scatter plot

  50. Body Fat Example: Correlation proccorrdata=bodyfatnoprob;run;

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