STAT302: Secs 102 & 103Summer I 1998Exam #4Fo r m AInstructor: Julie Hagen Carroll1. Don’t even open this until you are told to do so.2. Be sure to mark your section number (102 or 103) and your test form (A, B, C or D) on the scantron!3. Sign your name where indicated on your scantron and write your Wednesday section number andcomputer number beside it. Also, you must place your scantron in the correct section stack (for nextTuesday).4. There are 20 multiple-choice questions on this exam, each worth 5 points. There is partial credit. Pleasemark your answers clearly on the scantron. Multiple marks will be counted wrong.5. You will have 60 minutes to finish this exam.6. If you are caught cheating or helping someone to cheat on this exam, you both will receive a grade ofzero on the exam. You must work alone.7. This exam is worth 100 points, and will constitute 25% of your final grade.8. Good luck!1STAT302: 102&103 Exam #4, Form A Summer I 1998Number of obs = 55F( 1, 53) = 2.67Prob > F = 0.1082R-squared = 0.0480Adj R-squared = 0.0300Root MSE = 1.7777Source | SS df MS---------+------------------------------Model | 8.43720904 1 8.43720904Residual | 167.490064 53 3.16018988---------+------------------------------Total | 175.927273 54 3.25791246------------------------------------------------Age | Coef. S.E. t P>|t| [95% C.I.]---------+--------------------------------------ShoeSize | .180 .110 1.634 0.108 -.041 .4003_cons | 19.5 1.12 17.400 0.000 17.21 21.69------------------------------------------------1. What is the best conclusion that may be madebased on the output above?A. Since the p-value = 0.000, the regressionequation is better at predicting the y’s thanthe average y’s.B. Since the R2=0.0480, at the 5 and 10%levels the regression equation is better atpredicting the y’s than the average y’s.C. Since the p-value = 0.000, the regressionequation is 0.D. Since the p-value = 0.108, the regressionequation is not any better at predicting they’s than the average y’s.E. Since the p-value = 0.108, the regressionequation is any better at predicting the y’sthan the average y’s.2. What is the prediction (least squares) equationfor the output above?A.bShoeSize =0.180 + 19.5B.bShoeSize =0.180 + 19.5 ∗ AgeC.bAge =0.180 + 19.5 ∗ ShoeSizeD.bAge =19.5+0.180 ∗ ShoeSizeE.bShoeSize =19.5+0.180 ∗ Age3. What would happen if we added the point(20,40)?A. sewould increase and R2would decreaseB. sewould decrease and R2would increaseC. sewould increase and R2would not changeD. It’s is likely that a ShoeSize of 20 is outsidethe valid range of the model, and we cannotassume the relationship is still linear.E. None of the above4. What is the total variance of Age in the outputabove?A. It is not given in this output.B. 175.93C. 8.44D. 3.16E. 3.265. Why should we run a Two-Way ANOVA ratherthan just two One-Way ANOVA’s?A. We are likely to explain more of the varia-tion.B. We can always test the interaction, too.C. Two-Way uses the less data.D. All of the above.E. Exactly two of the above.Analysis of VarianceSource SS df MS F Prob > F---------------------------------------------------Between groups 1.9152113 3 .638404 3.32 0.0274Within groups 9.43046516 49 .192458---------------------------------------------------Total 11.3456765 52 .218186Bartlett’s test for equal variances:chi2(3)= 4.2899 Prob>chi2 = 0.2326. What should we say about the treatment (group)effect in the ANOVA table above?A. There is only a 2.74% probability that theeffect exists.B. The effect is only 2.74% significant.C. The effect is significant at the 5 and 10%levels.D. There is a 23.3% probability that the effectexists.E. The effect is not significant.7. In reference to the ANOVA table above, we as-sume the variances within each group are equal.What is our estimate of this variance?A. We don’t assume the variances are equalsince the p-value is less than 0.10.B. 9.43C. 11.3D. 0.218E. 0.1922STAT302: 102&103 Exam #4, Form A Summer I 1998AB8. Which of the residual plots above indicate thatthere is a possible influential point in the data?A. AB. BC. Both plots show points that should bedeleted.D. Both plots indicate an influential point.E. Both plots indicate an outlier in the data.9.Whydoweuseα=0.10 for Barlett’s test forequal variances?A. Because a Type I error would mean we didan invalid F -test.B. Because a Type I error would mean weclaim there is an effect when there isn’t any.C. Because a Type II error would mean we didan invalid F -test.D. Because a Type II error would mean weclaim there is an effect when there isn’t any.E. Because Barlett’s test is very conservative.10. Suppose you want to test the significance of theslope in a simple linear regression equation, butthe only information you have are 3 confidenceintervals for β1: (.295,4.305), (-0.119,4.719), (-0.978,5.578). What is the range of the p-valuefor testing H0: β1= 0 vs. HA: β16=0?A. pv > 0.10B. 0.10 > pv > 0.05C. 0.05 > pv > 0.01D. 0.01 > pvE. Confidence intervals only provide informa-tion when testing means.11. Suppose we are trying to predict y but the onlyx available has only a moderate correlation withy (the R2is around 50A. Multiply the y’s by a large number so theslope will increase.B. Divide the x’s by a large number so theslope will increase.C. Gather more data.D. All of the above.E. Exactly two of the above (excluding D.).12. What is the consequence of making a Type IIerror when testing the interaction in a Two-wayANOVA?A. We claim that the interaction is significantwhen it is not.B. We claim that the interaction exists whenit does not.C. We claim that there is no interaction whenthere is interaction.D. We claim that the variances are equal whenthey are not.E. Exactly two of the above.13. What does it mean to be statistically significantin reference to testing the true slope, β1=0?A. It means that the true slope is statisticallyequal to 0.B. It means that the estimated slope is statis-tically equal to β1.C. It means that regression model is a statisti-cally significant prediction equation for they’s.D. All of the above are correct.E. Exactly two of the above are correct.14. What does it mean to have a coefficient of deter-mination, R2=0?3STAT302: 102&103 Exam #4, Form A Summer I 1998A. There is no relationship between the x andy variables.B. The x’s are of no use in predicting the y’swith simple linear regression.C. The standard deviation of the regressionline, se=1.D. All of the above.E. Exactly two of the