S.E. of regression 8.303798 Akaike info criterion 7.073764Row SumsColumn SumsRow SumsColumn SumsRow SumsColumn SumsDec. 13, 2002 ECON 240A-1 L. PhillipsFinalAnswer 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, whetherthey 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 CharacteristicsDependent Variable: RETURNMethod: Least SquaresSample: 1 2029Included observations: 2029Variable Coefficient Std. Error t-Statistic Prob. C -1.147635 2.195444 -0.522735 0.6012TENURE 0.081806 0.175535 0.466039 0.6412SAT 0.005074 0.001281 3.959414 0.0001MBA 0.674400 0.375960 1.793809 0.0730AGE -0.140574 0.042422 -3.313715 0.0009R-squared 0.015083 Mean dependent var -0.554485Adjusted R-squared 0.013136 S.D. dependent var 8.358881S.E. of regression 8.303798 Akaike info criterion 7.073764Sum squared resid 139561.0 Schwarz criterion 7.087602Log likelihood -7171.334 F-statistic 7.748637Durbin-Watson stat 1.926228 Prob(F-statistic) 0.000003Use 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 L. PhillipsFinald. 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 DischargeOn DischargeOn Admission slight somewhat moderate Row Sumssevere 11 23 12 46considerable 9 10 4 23moderate 6 4 4 4Column Sums 26 37 20 83a. In the table below, fill in the expected cell counts (to one decimal point) underthe assumption of independence between disability on admission and disability on discharge.Table 1.2 Expected Cell Counts Under the Hypothesis of IndependenceOn DischargeOn Admission slight somewhat moderate Row Sumssevere 14.4 20.5 11.5considerable 7.2 10.3 5.5moderate 4.4 6.2 3.4Column Sumsb. 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 SquareOn DischargeOn Admission slight somewhat moderate Row Sumssevere 0.80 0.30 0.07considerable 0.45 0.01 0.41moderate 0.58 0.78 0.11Column SumsDec. 13, 2002 ECON 240A-3 L. PhillipsFinalc. 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? 4e. 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 ReplicationSUMMARY Form 1 Form 2 Form 3 Form 4 TotalLow Income: Group 1Count 10 10 10 10 40Sum 733 796 1006 1086 3621Average 73.3 79.6 100.6 108.6 90.525Variance 824.4556 648.2667 488.4889 753.1556 842.8712Middle Income Group 2Count 10 10 10 10 40Sum 957 905 1073 1100 4035Average 95.7 90.5 107.3 110 100.875Variance 863.3444 430.5 583.7889 1071.333 746.9327High Income Group 3Count 10 10 10 10 40Sum 1099 1100 1038 1115 4352Average 109.9 110 103.8 111.5 108.8Variance 660.9889 994.6667 881.0667 1601.833 964.0103TotalCount 30 30 30 30Sum 2789 2801 3117 3301Average 92.96667 93.36667 103.9 110.0333Variance 963.7575 807.0678 613.9552 1064.792ANOVASource of Variation SS df MS F P-value F critSample(Groups) 6718.717 2 3359.358 4.112707 0.018994 3.0803875Columns(Forms) 6279.867 3 2093.289 2.562717 0.058572 2.68869371Interaction 5101.883 6 850.3139 1.041 0.402973 2.18365415Within 88217 108 816.8241Total 106317.5 119Dec. 13, 2002 ECON 240A-4 L. PhillipsFinalUse 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 insignificantc. 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 significantd. 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. 0.00.20.40.60.81.00 2 4 6 8FVARDENSITY3.08 crit4.11Dec. 13, 2002 ECON 240A-5 L. PhillipsFinal4. (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 these firms was 9.2 years, average revenue was $ 4.25 million, and the average number of employees was 71. Three levels of planning were identified: (1) extensive with written long term
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