MTB > print c1 c2 c3 c4 c5 c6Data DisplayRow 3YRR 1YRR LOAD 3YRT 1YRT ASSETSMTB > print c6 c7 c9 c11 c13 c14 c15Data DisplayResults for: 252x07041-01A.MTWMTB > let c14 = c5*c3Stepwise Regression: 1YRR versus LOAD, 1YRT, ...Backward elimination. Alpha-to-Remove: 0.1Regression Analysis: 1YRR versus 1YRT, ASSETS, ...The regression equation isRegression Analysis: 1YRR versus LOAD, 1YRT, ASSETSThe regression equation isAnalysis of VarianceSource DF Seq SSRegression Analysis: 1YRR versus LOAD, 1YRT, 1YRTsq, ASSETSThe regression equation isAnalysis of VarianceSource DF Seq SSUnusual ObservationsRegression Analysis: 1YRR versus LOAD, ln1YRT, ASSETSThe regression equation isAnalysis of VarianceSource DF Seq SSRegression Analysis: 1YRR versus LOAD, 1YRT, 1YRTsq, ASSETSThe regression equation isAnalysis of VarianceSource DF Seq SSUnusual ObservationsRegression Analysis: 1YRR versus LOAD, 1YRT, 1YRTsq, ASSETS, ASSTsqThe regression equation isAnalysis of VarianceSource DF Seq SSRegression Analysis: 1YRR versus LOAD, 1YRT, 1YRTsq, lnAssetsThe regression equation isAnalysis of VarianceUnusual ObservationsRegression Analysis: 1YRR versus LOAD, 1YRT, 1YRTsq, ASSETS, ASSTsqThe regression equation isAnalysis of VarianceSource DF Seq SSRegression Analysis: 1YRR versus LOAD, 1YRT, ...The regression equation isAnalysis of VarianceUnusual ObservationsAnalysis of VarianceRegression Analysis: 1YRR versus LOAD, 1YRT, ...The regression equation isAnalysis of VarianceMTB > Name c16 "RESI1"Regression Analysis: 1YRR versus 1YRT, 1YRTsq, ...The regression equation isAnalysis of Variance9) a) So why am I very happy with Regression 9? (1.5)Solution: What happened in regressions 7 and 9 was that I removed ‘LOAD’ and added the interaction variable ‘1YRTL.’ While ‘LOAD’ never had a significant coefficient, all the coefficients now are significant.a) Why was I willing to accept a lower value of R-squared than in regression 8? (1)Solution: R-squared adjusted actually rose.b) Lets check out the effect of the signs of the coefficients? To start with we have what are essentially two equations here because of the interaction variables. What are they? (2)The regression equation isFor a Firm with no load ‘1YRTL’ and ‘AssetsL’ are zero so the equation reads as below.The regression equation isFor a firm with a load, we can add the coefficient of ‘1YRTL’ to the coefficient of ‘1YRT’ and add the coefficient of ‘AssetsL’ to the coefficient of ‘ASSETS.’The regression equation isWe have ‘1YRT’ = 58.2, ‘1YRTsq’ = 3387.24, ‘ASSETS’ = 247.01 and ‘Asstsq’ = 61013.94For a no-load firmFor a firm with a load= 162.54 – 158.43 + 65.42 – 179.32 + 115.26 = 5.47Minitab gets 5.54d) So how do rises of 10 in 1-year turnover and 10 in Assets affect these firms? You need four answers here. (4)After a rise of 10 in ‘1YRT’ we have ‘1YRT’ = 68.2, ‘1YRTsq’ = 4651.24, ‘ASSETS’ = 247.01 and ‘Asstsq’ = 61013.94For a no-load firmFor a firm with a loadAfter a rise of 10 in ‘ASSETS,’ we have ‘1YRT’ = 58.2, ‘1YRTsq’ = 3387.24, ‘ASSETS’ = 257.01 and ‘Asstsq’ = 66054.14For a no-load firmFor a firm with a loade) So, in view of d) are there any coefficients here that don’t seem reasonable? Why? (1.5) [25.5]Normplot of Residuals for 1YRRResidual Histogram for 1YRRProbability Plot of RESI1Probability Plot of RESI1Probability Plot of RESI1Best Subsets Regression: 1YRR versus 1YRT, 1YRTsq, ...Response is 1YRRA1 R Y S S eSaving file as: 'C:Documents and SettingsRBOVEMy252y0741 5/7/07ECO252 QBA2Final EXAMMay , 2007Version 1Name and Class hour:______KEY_______________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 AnywhereElse) 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 c6Data Display Row 3YRR 1YRR LOAD 3YRT 1YRT ASSETS 1 5.6 0.1 0 112 58 220.00 2 4.7 1.9 1 95 62 158.00 3 4.5 2.6 1 241 65 227.25 4 4.8 2.0 1 87 61 242.40 5 5.7 3.5 0 98 57 287.85 6 4.1 -4.3 1 102 66 207.05 7 4.7 3.2 1 72 63 237.35 8 4.1 -4.1 1 96 65 207.05 9 5.2 2.2 0 78 59 262.60 10 3.7 2.1 1 118 87 186.85 11 6.2 5.3 0 98 47 313.10 12 6.6 11.0 0 87 41 333.30 13 5.2 0.3 0 117 61 262.60 14 5.5 -2.1 0 87 46 277.75 15 5.6 4.7 0 85 35 282.00In 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 1- year 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 c15Data Display Row ASSETS ASSTsq lnAssets 1YRTsq AssetsL 1YRTL ln1YRT 1 220.00 48400 5.39363 3364 0.00 0 4.06044 2 158.00 24964 5.06260 3844 158.00 62 4.12713 3 227.25 51643 5.42605 4225 227.25 65 4.17439 4 242.40 58758 5.49059 3721 242.40 61 4.11087 5 287.85 82858 5.66244 3249 0.00 0 4.04305 6 207.05 42870 5.33296 4356 207.05 66 4.18965 7 237.35 56335 5.46954 3969 237.35 63 4.14313 8 207.05 42870 5.33296 4225 207.05 65 4.17439 9 262.60 68959 5.57063 3481 0.00 0 4.07754 10 186.85 34913 5.23031 7569 186.85 87 4.46591 11 313.10 98032 5.74652 2209 0.00 0 3.85015 12 333.30 111089 5.80904 1681 0.00 0 3.71357 13 262.60 68959 5.57063 3721 0.00 0 4.11087 14 277.75 77145 5.62672 2116 0.00 0 3.82864 15 282.00 79524
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