Quiz Practice Questions 5 (Attendance 10) for Statistics 512Applied Regression AnalysisMaterial Covered: Chapter 11 Neter et al. and KuhnBy: Friday, 7th November, Fall 2003These are practice questions for the quiz. The quiz (not the practice questions) isworth 5% and marked out of 5 points. One or more questions is closely, but notnecessarily exactly, related to one or more of these questions will appear on the quiz.These practice questions are not to be handed in. Quizzes are to be done using Vistaon the Internet before 4am of the date of the quiz. Vista will not allow any quizto be done late. It is highly recommended that you complete this practice quiz, byhand, before logging onto Vista. The quiz is an individual one which means thateach student does this quiz by themselves without help from others.1. Applied Linear Statistical Models(Neter et al.) Questions.Chapter Problem(s) hints11, pages 490–496 11.4, 11.8 Calculator Maintenance11.14 Assessed Valuations(11.4) Calculator Maintenance*PRACTICE QUIZ 5, 11.4 CALCULATOR; *QUALITATIVE, PP 490-496;DATA CALC; INPUT TIME NUMBER TYPEIND; NUMTYPE = NUMBER*TYPEIND;DATALINES;97 7 086 6 178 5 010 1 075 5 062 4 1101 7 139 3 053 4 033 2 0118 8 065 5 125 2 171 5 0105 7 117 1 049 4 068 5 0;PROC REG DATA=CALC ALPHA = 0.05; TITLE '11.4(A,B) QUALITATIVE REGRESSION'; MODEL TIME = NUMBER TYPEIND / SS1; OUTPUT OUT=CALC1 R=RESID;RUN;SYMBOL1 V=CIRCLE C=BLACK I=R;SYMBOL2 V=DOT C=BLACK I=R;PROC GPLOT DATA=CALC1; TITLE '11.4(E) RESIDUALS VS INTERACTION'; PLOT RESID*NUMTYPE=TYPEIND; *scatterplot of RESID vs NUMBER*TYPEIND;RUN;QUIT;(a) and (b) Regression For Qualitative Variables.The regression without interaction is given byˆY = b0+ b1X1+ b2X2= −2.3475 + 14.7234X1+ 0.2766X2= −2.3475 + 14.7234X1, if X2= 0 (commerical)= −2.0709 + 14.7234X1, if X2= 1 (student)whereb0average time of service call when zero (0) calculatorsb1average time needed to service one more calculatorb2how much more/less service time is spent oneither commerical calculators (when X2= 0)or student calculators (when X2= 1).It appears more service time is devoted to student calculators, rather thancommercial calculators because both are associated with the same regres-sion lines, except the regression line associated with the student calculatorscrosses at a higher y–intercept.(c) (Bonferroni) Confidence Intervals of β2s{b2} = 2.37811, t(0.975, 15) = 2.131(PRGM INVT ENTER ENTER 15 ENTER 0.975)then 95% CI is 0.2766 ± 2.131(2.37811) = (−4.791, 5.344)since this includes zero (0), calculator model is not influencing the averageservice time, or, in other words, there is no significant difference betweenstudent and commercial service time(d) Why include X1?The number of calculators is included in the regression because this, aswell as calculator model, influences service time. The regression describesthe data better with calculator model included than if calculator model isnot included.(e) Residuals Versus Interaction, X1X2Attached residual plot is (more or less) a band and so indicates there is nointeraction.(11.8) Calculator Maintenance*PRACTICE QUIZ 5, 11.8 CALCULATOR; *QUALITATIVE INTERACTIVE, PP 490-496;DATA CALC; INPUT TIME NUMBER TYPEIND; NUMTYPE = NUMBER*TYPEIND;DATALINES;97 7 086 6 178 5 010 1 075 5 062 4 1101 7 139 3 053 4 033 2 0118 8 065 5 125 2 171 5 0105 7 117 1 049 4 068 5 0;PROC REG DATA=CALC ALPHA = 0.10; TITLE '11.8, CALCULATOR MAINTANENCE WITH INTERACTION'; MODEL TIME = NUMBER TYPEIND NUMTYPE / SS1;RUN;QUIT;(a) Regression With Interaction.ˆY = −1.56 + 14.54X1− 3.17X2+ 0.7X1X2(b) Test if interaction term can be dropped.Source Sum Of Squares Degrees of Freedom Mean SquaresRegression 16190 3 5396.57X116183 1 16183X2|X10.28959 1 0.28959X1X2|X1, X26.8299 1 6.8299Error 314.276 14 22.44831Total 16504 171. Statement.H0: β12= 0 versus H0: β126= 0where we assumeY = β1X1+ β2X2+ β12X1X2+ ε2. Test.The partial F∗test statistic isF∗=SSE(R) − SSE (F )dfR− dfF÷SSE(F )dfF=SSE(X1X2) − SSE(X1, X2, X1X2)(n − 3) − (n − 4)÷SSE(X1, X2, X1X2)n − 4=SSR(X1X2|X1, X2)1÷SSE(X1, X2, X1X2)n − 4=6.82991÷314.276414= 0.30The upper critical value at α = 0.10,with (1, 14) degrees of freedom is 3.10(Use PRGM INVF ENTER 1 ENTER 14 ENTER 0.90 ENTER)3. Conclusion.Since the test statistic, 0.30, is smaller than the critical value, 3.10, weaccept the null hypothesis that the interaction term is zero, β12= 0.(11.14) Assessed Valuation*PRACTICE QUIZ 5, 11.14 VALUATIONS; *TWO QUALITATIVE VARIABLES, PP 490-496;DATA HOME; INPUT PRICE VALUE LOTIND; VALLOT = VALUE*LOTIND;DATALINES;56.2 17.5 142.5 12.5 168.6 20 154.8 16 150 15 147.5 14.7 156.9 17.5 134 12.3 139 11.5 131.2 10 036.9 13.8 041 15 051.8 19.5 048 17 033.3 12.5 038 14.5 035.9 12.8 032 12 044.3 16 029 10 046.1 17 030 10.8 042 15 0;SYMBOL1 V=CIRCLE C=BLACK I=R;SYMBOL2 V=DOT C=BLACK I=R;PROC GPLOT DATA=HOME; TITLE '11.14(A), SCATTER PLOTS'; PLOT PRICE*VALUE=LOTIND; *scatterplot of PRICE vs VALUE with TYPEIND as an indicator;RUN;PROC REG DATA=HOME ALPHA = 0.10; TITLE '11.14(B), TEST B2 = B12 = 0'; MODEL PRICE = VALUE LOTIND VALLOT / SS1;RUN;DATA HOMECORNER; SET HOME; IF LOTIND = 1;RUN;PROC REG DATA=HOMECORNER; TITLE '11.14(C) REGRESSION, HOMES ON CORNERS'; MODEL PRICE = VALUE; OUTPUT OUT=CORNERPLOT R=CORNERRESID P=CORNERPRED;RUN;DATA HOMENONCORNER; SET HOME; IF LOTIND = 0;RUN;PROC REG DATA=HOMENONCORNER; TITLE '11.14(C) REGRESSION, HOMES NOT ON CORNERS'; MODEL PRICE = VALUE; OUTPUT OUT=NONCORNERPLOT R=NONCORNERRESID P=NONCORNERPRED;RUN;PROC REG DATA=HOME ALPHA = 0.10; TITLE '11.14(D) CI FOR INTERACTION'; MODEL PRICE = VALUE LOTIND VALLOT;RUN;SYMBOL1 V=CIRCLE C=BLACK I=R;SYMBOL2 V=DOT C=BLACK I=R;PROC GPLOT DATA=CORNERPLOT; TITLE '11.14(E) RESIDUALS VS Y, HOMES ON CORNERS'; PLOT CORNERRESID*CORNERPRED; RUN;PROC GPLOT DATA=NONCORNERPLOT; TITLE '11.14(E) RESIDUALS VS Y, HOMES NOT ON CORNERS'; PLOT NONCORNERRESID*NONCORNERPRED; RUN;PROC REG DATA=HOMECORNER; TITLE '11.14(F) S_1^2 = MSE, HOMES ON CORNERS'; MODEL PRICE = VALUE;RUN;PROC REG DATA=HOMENONCORNER; TITLE '11.14(F) S_2^2 = MSE, HOMES NOT ON CORNERS'; MODEL PRICE = VALUE;RUN;PROC REG DATA=HOMENONCORNER OUTEST=EST NOPRINT; TITLE '11.14(G) VARIOUS RESIDUAL PLOTS, ALL DATA'; MODEL PRICE = VALUE LOTIND VALLOT; OUTPUT OUT=OUTPLOT R=RESID