STAT302 Secs 102 103 Summer I 1998 Exam 4 Form A Instructor Julie Hagen Carroll 1 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 and computer number beside it Also you must place your scantron in the correct section stack for next Tuesday 4 There are 20 multiple choice questions on this exam each worth 5 points There is partial credit Please mark 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 of zero 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 1 Exam 4 Form A STAT302 102 103 Number of obs F 1 53 Prob F R squared Adj R squared Root MSE 4 What is the total variance of Age in the output above 55 2 67 0 1082 0 0480 0 0300 1 7777 A B C D E Source SS df MS Model 8 43720904 1 8 43720904 Residual 167 490064 53 3 16018988 Total 175 927273 54 3 25791246 It is not given in this output 175 93 8 44 3 16 3 26 5 Why should we run a Two Way ANOVA rather than just two One Way ANOVA s 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 A We are likely to explain more of the variation 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 1 What is the best conclusion that may be made based on the output above A Since the p value 0 000 the regression equation is better at predicting the y s than the average y s B Since the R2 0 0480 at the 5 and 10 levels the regression equation is better at predicting the y s than the average y s C Since the p value 0 000 the regression equation is 0 D Since the p value 0 108 the regression equation is not any better at predicting the y s than the average y s E Since the p value 0 108 the regression equation is any better at predicting the y s than the average y s Analysis of Variance Source SS df MS F Prob F Between groups 1 9152113 3 638404 3 32 0 0274 Within groups 9 43046516 49 192458 Total 11 3456765 52 218186 Bartlett s test for equal variances chi2 3 4 2899 Prob chi2 0 232 6 What should we say about the treatment group effect in the ANOVA table above A There is only a 2 74 probability that the effect 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 effect exists E The effect is not significant 2 What is the prediction least squares equation for the output above A B C D E Summer I 1998 b ShoeSize 0 180 19 5 b ShoeSize 0 180 19 5 Age b 0 180 19 5 ShoeSize Age b 19 5 0 180 ShoeSize Age b ShoeSize 19 5 0 180 Age 3 What would happen if we added the point 20 40 7 In reference to the ANOVA table above we assume the variances within each group are equal What is our estimate of this variance se would increase and R2 would decrease se would decrease and R2 would increase se would increase and R2 would not change It s is likely that a ShoeSize of 20 is outside the valid range of the model and we cannot assume the relationship is still linear E None of the above A We don t assume the variances are equal since the p value is less than 0 10 B 9 43 C 11 3 D 0 218 E 0 192 A B C D 2 STAT302 102 103 Exam 4 Form A Summer I 1998 10 Suppose you want to test the significance of the slope in a simple linear regression equation but the only information you have are 3 confidence intervals for 1 295 4 305 0 119 4 719 0 978 5 578 What is the range of the p value for testing H0 1 0 vs HA 1 6 0 A B C D E pv 0 10 0 10 pv 0 05 0 05 pv 0 01 0 01 pv Confidence intervals only provide information when testing means 11 Suppose we are trying to predict y but the only x available has only a moderate correlation with y the R2 is around 50 A A Multiply the y s by a large number so the slope will increase B Divide the x s by a large number so the slope 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 II error when testing the interaction in a Two way ANOVA A We claim that the interaction is significant when it is not B We claim that the interaction exists when it does not C We claim that there is no interaction when there is interaction D We claim that the variances are equal when they are not E Exactly two of the above B 8 Which of the residual plots above indicate that there is a possible influential point in the data A A B B C Both plots show points that should be deleted D Both plots indicate an influential point E Both plots indicate an outlier in the data 13 What does it mean to be statistically significant in reference to testing the true slope 1 0 9 Why do we use 0 10 for Barlett s test for equal variances A It means that the true slope is statistically equal to 0 B It means that the estimated slope is statistically equal to 1 C It means that regression model is a statistically significant prediction equation for the y s D All of the above are correct E Exactly two of the above are correct A Because a Type I error would mean we did an invalid F test B Because a Type I error would mean we claim there is an effect when there isn t any C Because a Type II error would mean we did an invalid F test D Because a Type II error would mean we claim there is an effect when there isn t any E Because Barlett …