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 SetC2 X2 Type 1 = Private, 0 = Public.C3 X1 First Quartile SATC3 X5 3rd Quartile SATC5 X4 Room and Board CostC6 Y Annual Total CostC7 X6 Average Indebtedness at GraduationC8 X3 Interaction = X1 * X2You 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 220ˆXbbY . a)According to the first regression in regression 2 what are the mean annual total costs for publicand 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 0b1013 and the slope, relative to the first quartile SAT is 1b11.3339. The equation relating annual total costs to the first quartile SAT effectivelyhas 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 es 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 12/06/03Retrieving worksheet from file: C:\Documents and Settings\RBOVE.WCUPANET\My Documents\Drive D\MINITAB\Colleges2002.MTW# Worksheet was saved on Fri Dec 05 2003Results for: Colleges2002.MTWMTB > 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 = 80 Step 1 2Constant 12198 -1021inter 10.42 8.35T-Value 17.40 11.97P-Value 0.000 0.000First qu 13.3T-Value 4.62P-Value 0.000S 3058 2724R-Sq 79.51 83.95R-Sq(adj) 79.25 83.54C-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> noMTB > 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 = 80 Step 1 2 3Constant 12478 -7264 1013Type of 11646 8732 -3016T-Value 13.97 11.57 -0.48P-Value 0.000 0.000 0.630First qu 19.5 11.3T-Value 7.37 2.25P-Value 0.000 0.027inter 11.2T-Value 1.90P-Value 0.061S 3610 2783 2737R-Sq 71.44 83.24 84.00R-Sq(adj) 71.07 82.81 83.37C-p 58.1 4.7 3.12More? (Yes, No, Subcommand, or Help) SUBC> yes3252x0343 12/06/03 No variables entered or removed More? (Yes, No, Subcommand, or Help)SUBC> noMTB > 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 SchoThe regression equation isAnnual Total Cost = - 7264 + 19.5 First quartile SAT + 8732 Type of SchoolPredictor Coef SE Coef T P VIFConstant -7264 2728 -2.66 0.009First qu 19.524 2.651 7.37 0.000 1.4Type of 8732.4 754.7 11.57 0.000 1.4S = 2783 R-Sq = 83.2% R-Sq(adj) = 82.8%Analysis of VarianceSource DF SS MS F PRegression 2 2963313624 1481656812 191.26 0.000Residual Error 77 596492779 7746659Total 79 3559806404Source DF Seq SSFirst qu 1 1926306635Type of 1 1037006989Unusual ObservationsObs First qu Annual T
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