252x0343 12 06 03 ECO252 QBA2 Name FINAL EXAM Hour of Class Registered DEC 11 2003 I 25 points Do all the following Note that answers without reasons receive no credit Most answers require a statistical test that is stating or implying a hypothesis and showing why it is true or false by citing a table value or a p value The fourth computer problem involved the regression of the Y variable below against some but not all of the X values Column Variables in Data Set C2 X2 Type 1 Private 0 Public C3 X1 First Quartile SAT C3 X5 3rd Quartile SAT C5 X4 Room and Board Cost C6 Y Annual Total Cost C7 X6 Average Indebtedness at Graduation C8 X3 Interaction X1 X2 You were directed to hand in the computer output 4 points and your answer to problem 14 37 or the equivalent problem in the 8th edition Up to 7 points I ran the same problem you did but went on to add X4 and X5 to the input The output appears on pages 1 7 My first two regressions were stepwise regressions The second stepwise regression is set up to force the dummy variable designating type of university into the equation This means that our first equation in regression 2 is essentially Y b0 b2 X 2 a According to the first regression in regression 2 what are the mean annual total costs for public and private universities and how does the printout show us that they are significantly different 2 b Regressions 3 and 4 are the regressions you supposedly did According to this regression for a public university the constant in the regression equation is b0 1013 and the slope relative to the first quartile SAT is b1 11 3339 The equation relating annual total costs to the first quartile SAT effectively has both a different intercept and a different slope what is the equation Are the intercepts and slopes for public and private universities in fact significantly different What tells us this 3 Extra credit at what SAT level do public and private universities have the same cost 2 c Regression 6 should be the best of all the regressions because it has the most independent variables and the highest R squared but it isn t i Look at the coefficients of the independent variables and ignore their significance one of those coefficients is incredibly unreasonable which one is it 1 ii Which coefficients are significant at the 1 level why 2 What about the 10 level 1 Compare the adjusted R squares with the other regressions what do they tell us 1 Look at the VIFs what do they imply 2 d Do an F test to tell whether adding X3 X4 and X5 as a package to equation 3 with only X1 and X2 was useful What is your conclusion 4 e I didn t follow directions when I did a prediction interval for equation 3 so it should disagree with yours I added some guesses as to median values for X3 X4 and X5 What does the printout say I used What would you expect should happen to the size of the prediction interval if our addition of new variables gives us a better estimate of Y Did it happen Cite numbers 3 f Use the method suggested in the text using the standard error s e to compute a prediction interval for the same values of the independent variables and equation 3 how accurate is it 3 32 12 5 2003 7 15 10 PM Welcome to Minitab press F1 for help MTB Retrieve C Documents and Settings RBOVE WCUPANET My Documents Drive D MINITAB Colleges2002 MTW 252x0343 12 06 03 Retrieving worksheet from file C Documents and Settings RBOVE WCUPANET My Documents Drive D MINITAB Colleges2002 MTW Worksheet was saved on Fri Dec 05 2003 Results for Colleges2002 MTW MTB Stepwise c6 c3 c2 c8 c5 c4 SUBC AEnter 0 15 SUBC ARemove 0 15 SUBC Constant 1 Stepwise Regression Annual Total versus First quarti Type of Scho Alpha to Enter 0 15 Alpha to Remove 0 15 Response is Annual T on 5 predictors with N Step Constant 1 12198 2 1021 inter T Value P Value 10 42 17 40 0 000 8 35 11 97 0 000 First qu T Value P Value 80 13 3 4 62 0 000 S 3058 2724 R Sq 79 51 83 95 R Sq adj 79 25 83 54 C p 20 2 1 3 More Yes No Subcommand or Help SUBC yes No variables entered or removed More Yes No Subcommand or Help SUBC no MTB Stepwise c6 c3 c2 c8 c5 c4 SUBC Force c2 SUBC AEnter 0 15 SUBC ARemove 0 15 SUBC Constant 2 Stepwise Regression Annual Total versus First quarti Type of Scho Alpha to Enter 0 15 Alpha to Remove 0 15 Response is Annual T on 5 predictors with N Step Constant 1 12478 2 7264 3 1013 Type of T Value P Value 11646 13 97 0 000 8732 11 57 0 000 3016 0 48 0 630 19 5 7 37 0 000 11 3 2 25 0 027 First qu T Value P Value inter T Value P Value S R Sq R Sq adj C p 80 11 2 1 90 0 061 3610 71 44 71 07 58 1 2783 83 24 82 81 4 7 2737 84 00 83 37 3 1 2 More Yes No Subcommand or Help SUBC yes 3 252x0343 12 06 03 No variables entered or removed More Yes No Subcommand or Help SUBC no MTB Name c18 RESI1 MTB Regress c6 2 c3 c2 SUBC Residuals RESI1 SUBC GHistogram SUBC GNormalplot SUBC GFits SUBC RType 1 SUBC Constant SUBC VIF SUBC Predict c9 c10 SUBC Brief 2 3 Regression Analysis Annual Total versus First quarti Type of Scho The regression equation is Annual Total Cost 7264 19 5 First quartile SAT 8732 Type of School Predictor Constant First qu Type of Coef 7264 19 524 8732 4 S 2783 SE Coef 2728 2 651 754 7 R Sq 83 2 T 2 66 7 37 11 57 P 0 009 0 000 0 000 VIF 1 4 1 4 R Sq adj 82 8 Analysis of Variance Source Regression Residual Error Total Source First qu Type of DF 1 1 DF 2 77 79 SS 2963313624 596492779 3559806404 MS 1481656812 7746659 F 191 26 P 0 000 Seq SS 1926306635 1037006989 Unusual Observations Obs First qu Annual T 27 1040 21484 56 1010 15722 61 1320 17526 Fit 13041 21188 27240 SE Fit 514 560 578 Residual 8443 5466 9714 St Resid 3 09R 2 00R 3 57R R denotes an observation with a large standardized residual Predicted Values for New Observations New Obs 1 Fit 20993 SE Fit 579 95 0 CI 19839 22147 95 0 PI 15332 26654 Values of Predictors for New Observations New Obs 1 First qu 1000 Type of 1 00 Residual Histogram for Annual T Normplot of Residuals for Annual T Residuals vs Fits for Annual T MTB Resplots c18 c2 SUBC …
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