252x0741 5 8 07 ECO252 QBA2 Final EXAM May 2007 Version 1 Name and Class hour I 18 points Do all the following Note that answers without reasons and citation of appropriate statistical tests 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 If you haven t done it lately take a fast look at ECO 252 Things That You Should Never Do on a Statistics Exam or Anywhere Else In his text Allen L Webster presents the following data The hope was to explain three year returns of the funds and to compare them to one year returns The data given is as follows MTB print c1 c2 c3 c4 c5 c6 Data Display Row 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 3YRR 5 6 4 7 4 5 4 8 5 7 4 1 4 7 4 1 5 2 3 7 6 2 6 6 5 2 5 5 5 6 1YRR 0 1 1 9 2 6 2 0 3 5 4 3 3 2 4 1 2 2 2 1 5 3 11 0 0 3 2 1 4 7 LOAD 0 1 1 1 0 1 1 1 0 1 0 0 0 0 0 3YRT 112 95 241 87 98 102 72 96 78 118 98 87 117 87 85 1YRT 58 62 65 61 57 66 63 65 59 87 47 41 61 46 35 ASSETS 220 00 158 00 227 25 242 40 287 85 207 05 237 35 207 05 262 60 186 85 313 10 333 30 262 60 277 75 282 00 In the above 1YRR is the rate of return over a 1 year period LOAD is a dummy variable that is 1 when there is a load and zero if it is a no load fund 1YRT is a turnover rate for the fund and tells you the percent of the fund bought or sold during the year ASSETS is the assets in billions when the fund opened The remaining columns are for 3 year data and are not used here I played with these data for a while and got very discouraging results for the 3 rear data and nearly as discouraging results for the 1year data as you will see in Regression 3 below I finally created the set of new independent variables that appear below MTB print c6 c7 c9 c11 c13 c14 c15 Data Display Row 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ASSETS 220 00 158 00 227 25 242 40 287 85 207 05 237 35 207 05 262 60 186 85 313 10 333 30 262 60 277 75 282 00 ASSTsq 48400 24964 51643 58758 82858 42870 56335 42870 68959 34913 98032 111089 68959 77145 79524 lnAssets 5 39363 5 06260 5 42605 5 49059 5 66244 5 33296 5 46954 5 33296 5 57063 5 23031 5 74652 5 80904 5 57063 5 62672 5 64191 1YRTsq 3364 3844 4225 3721 3249 4356 3969 4225 3481 7569 2209 1681 3721 2116 1225 AssetsL 0 00 158 00 227 25 242 40 0 00 207 05 237 35 207 05 0 00 186 85 0 00 0 00 0 00 0 00 0 00 1YRTL 0 62 65 61 0 66 63 65 0 87 0 0 0 0 0 ln1YRT 4 06044 4 12713 4 17439 4 11087 4 04305 4 18965 4 14313 4 17439 4 07754 4 46591 3 85015 3 71357 4 11087 3 82864 3 55535 1 252x0741 5 8 07 ASSTsq is the square of the ASSETS variable lnASSETS is the natural logarithm of the ASSETS variable 1YRTsq is the square of the one year turnover AssetsL is an interaction variable the product of ASSETS and LOAD 1YRTL is the product of 1YRT and LOAD Ln1YRT is the natural logarithm of 1YRT 5 1 2007 9 16 52 PM Welcome to Minitab press F1 for help Results for 252x07041 01A MTW MTB let c14 c5 c3 MTB Stepwise c2 c3 c5 c6 c7 c9 c11 c13 c14 SUBC Backward SUBC ARemove 0 1 SUBC Best 0 SUBC Constant Regression 1 Stepwise Regression 1YRR versus LOAD 1YRT Backward elimination Alpha to Remove 0 1 Response is 1YRR on 8 predictors with N 15 Step Constant 1 1485 2 1458 3 1099 LOAD T Value P Value 2 0 04 0 971 1YRT T Value P Value 2 08 1 74 0 132 2 12 3 65 0 008 2 10 3 81 0 005 ASSETS T Value P Value 1 80 0 84 0 432 1 75 1 11 0 303 0 96 5 37 0 001 ASSTsq T Value P Value 0 0009 0 41 0 698 0 0008 0 50 0 630 332 1 23 0 265 325 1 73 0 127 234 5 03 0 001 1YRTsq T Value P Value 0 0216 1 74 0 133 0 0221 3 81 0 007 0 0218 3 98 0 004 AssetsL T Value P Value 0 256 2 23 0 067 0 253 3 73 0 007 0 251 3 90 0 005 1YRTL T Value P Value 0 92 1 26 0 255 0 94 3 61 0 009 0 94 3 79 0 005 S R Sq R Sq adj Mallows C p 2 03 87 79 71 51 9 0 1 88 87 79 75 57 7 0 1 79 87 34 77 85 5 2 lnAssets T Value P Value More Yes No Subcommand or Help SUBC y No variables entered or removed 2 252x0741 5 8 07 More Yes No Subcommand or Help SUBC n 1 Regression 1 is a reverse stepwise equation that I ran on the full model to see if there were any obvious candidates for elimination The third column is the 3 rd regression that was run What can you say about the significance of the coefficients of the variables that stepwise forced out Why Do any of the variables left in have a suspicious sign 2 MTB Regress c2 6 SUBC Constant SUBC VIF SUBC Brief 2 c5 c6 Regression 2 c9 c11 c13 c14 Regression Analysis 1YRR versus 1YRT ASSETS The regression equation is 1YRR 1099 2 10 1YRT 0 962 ASSETS 234 0 251 AssetsL 0 945 1YRTL Predictor Coef SE Coef T P Constant 1098 8 220 7 4 98 0 001 1YRT 2 1015 0 5518 3 81 0 005 ASSETS 0 9623 0 1792 5 37 0 001 lnAssets 233 89 46 50 5 03 0 001 1YRTsq 0 021819 0 005488 3 98 0 004 AssetsL 0 25128 0 06438 3 90 0 005 1YRTL 0 9446 0 2491 3 79 0 005 S 1 79353 R Sq 87 3 Analysis of Variance Source DF SS Regression 6 177 595 Residual Error 8 25 734 Total 14 203 329 Source 1YRT ASSETS lnAssets 1YRTsq AssetsL 1YRTL DF 1 1 1 1 1 1 lnAssets 0 …
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