Dec 13 2002 ECON 240A 1 Final L Phillips Answer all four questions 1 40 points Researchers at the National Bureau of Economic Research collected data on the rate of return net of the risk free rate r for 2029 mutual funds as well as personal data on the fund managers The latter included age their tenure as fund manager whether they had an MBA or not a zero one dummy variable yes one and the average SAT score for the school where the manager had received an undergraduate degree The regression estimated was r j c 1 c 2 tenure j c 3 SAT j c 4 MBA j c 5 age j e j The residuals from this regression were not significantly different from normal The estimation results follow Table 1 1 Regression Results Net Rate of Return for Mutual Funds Vs Fund Manager Characteristics Dependent Variable RETURN Method Least Squares Sample 1 2029 Included observations 2029 Variable C TENURE SAT MBA AGE Coefficient 1 147635 0 081806 0 005074 0 674400 0 140574 R squared Adjusted R squared S E of regression Sum squared resid Log likelihood Durbin Watson stat 0 015083 0 013136 8 303798 139561 0 7171 334 1 926228 Std Error 2 195444 0 175535 0 001281 0 375960 0 042422 t Statistic 0 522735 0 466039 3 959414 1 793809 3 313715 Mean dependent var S D dependent var Akaike info criterion Schwarz criterion F statistic Prob F statistic Prob 0 6012 0 6412 0 0001 0 0730 0 0009 0 554485 8 358881 7 073764 7 087602 7 748637 0 000003 Use a 5 level for a type I error a Is the regression as a whole significant Yes F statistic is highly signifacant b Which of the explanatory variables are insignificant Tenure and MBA if you do a 2 tail test c Which is the most significant of the explanatory variables What is the economic significance of these statistical results SAT Quality of school increases net return and age decreases net return Dec 13 2002 ECON 240A 2 Final L Phillips d Do these variables characterizing the mutual fund managers explain very much of the variation in the net rate of return for mutual funds No R2 is only 0 015 2 40 points Patients were admitted to Massachusetts General Hospital following a stroke Their physical disability was assessed on admission and also upon discharge No patient was discharged with a worse assessment than upon admission The question is whether the patient s disability level upon discharge was related to his her disability level at admission The data were adapted from Bishop Fienberg and Holland Discrete Multivariate Analysis Table 1 1 Cross Tabulation of Patient s Disability On Admission with Disability On Discharge On Discharge On Admission slight somewhat moderate Row Sums severe 11 23 12 46 considerable 9 10 4 23 moderate 6 4 4 4 Column Sums 26 37 20 83 a In the table below fill in the expected cell counts to one decimal point under the assumption of independence between disability on admission and disability on discharge Table 1 2 Expected Cell Counts Under the Hypothesis of Independence On Admission severe considerable moderate Column Sums On Discharge slight somewhat 14 4 20 5 7 2 10 3 4 4 6 2 moderate 11 5 5 5 3 4 Row Sums b In the table below using Pearson s Chi Square statistic calculate each cell s contribution to Chi Square to the second decimal point Table 1 3 Each Cell s Contribution to Pearson s Chi Square On Admission severe considerable moderate Column Sums On Discharge slight somewhat 0 80 0 30 0 45 0 01 0 58 0 78 moderate 0 07 0 41 0 11 Row Sums Dec 13 2002 ECON 240A 3 Final L Phillips c What is the numerical value of the Chi Square statistic for testing independence 3 43 the sum of nine entries in Table 1 3 d How many degrees of freedom does it have 4 e At the 5 level for a type I error do you reject the null hypothesis of independence No chi square critical is 9 49 for 4 degrees of freedom at 5 3 40 points The number of minutes it takes to fill out four versions of an IRS form was recorded for three different groups with ten taxpayers in each group group 1 is the low income bracket group 2 is the middle income bracket and group 3 is the high income bracket The descriptive statistics and Table of ANOVA follow Anova Two Factor With Replication SUMMARY Form 1 Form 2 Form 3 Form 4 Total Low Income Group 1 Count Sum Average Variance 10 10 10 10 40 733 796 1006 1086 3621 73 3 79 6 100 6 108 6 90 525 824 4556 648 2667 488 4889 753 1556 842 8712 Middle Income Group 2 Count Sum Average Variance 10 957 95 7 863 3444 10 10 10 40 905 1073 1100 4035 90 5 107 3 110 100 875 430 5 583 7889 1071 333 746 9327 High Income Group 3 Count Sum Average Variance 10 10 10 10 40 1099 1100 1038 1115 4352 109 9 110 103 8 111 5 108 8 660 9889 994 6667 881 0667 1601 833 964 0103 Total Count Sum Average Variance 30 30 30 30 2789 2801 3117 3301 92 96667 93 36667 103 9 110 0333 963 7575 807 0678 613 9552 1064 792 ANOVA Source of Variation Sample Groups Columns Forms Interaction Within SS 6718 717 6279 867 5101 883 88217 Total 106317 5 df 2 3 6 108 119 MS F P value 3359 358 4 112707 0 018994 2093 289 2 562717 0 058572 850 3139 1 041 0 402973 816 8241 F crit 3 0803875 2 68869371 2 18365415 Dec 13 2002 ECON 240A 4 Final L Phillips Use a 5 level for a type I error a Is there any significant interaction in determining the average time to complete a form between the income level of the taxpayer and the design of the form No F of 1 04 is insignificant b Is there any significant difference in the average time to fill out a form attributable to the design of the form No F of 2 56 is insignificant c Is there any significant difference in the average time to complete a form attributable to the income level of the taxpayer Yes F of 4 11 is significant d On the chart of the F distribution below for 2 and 108 degrees of freedom illustrate the F statistic value used to test the significance of the income level of the taxpayer in part c above and the critical value for this f distribution at the 5 level 1 0 DENSITY 0 8 0 6 0 4 0 2 0 0 0 23 08 crit 4 4 11 FVAR 6 8 Dec 13 2002 ECON 240A 5 Final L Phillips 4 40 points In a study of the importance of planning for small business a random sample of 73 firms was taken The average age for …
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