Dec 9 2003 ECON 240A 1 Final L Phillips Answer all five questions Each question is worth 30 points 1 A survey of economics econometrics students was conducted about the monthly rent per person that they paid along with the information about the number of persons living together the number of rooms in the unit the number of blocks from the center of campus and the gender of the person responding female 1 for yes 0 for no The 32 observations of data is appended to the exam Figure 1 1 shows the histogram and descriptive statistics for rent per person Figure 1 2 depicts a regression of rent per person against the number of persons living together in the unit a Is this cross section or time series data Cros section Figure 1 1 His togram and Statis tic s for Rent Per Pers on 10 Series RENTPERPERSON Sample 1 32 Obs erv ations 32 8 6 4 Mean Median Max imum Minimum Std Dev Skewnes s Kurtosis 138 1693 140 0000 285 0000 50 75000 47 11474 1 017101 4 787240 J arque Bera Probability 9 776269 0 007535 2 0 50 75 100 125 150 175 200 225 250 275 300 b Is the distribution more or less symmetric Yes but a little skewed and kurtotic c Is it normally distributed Explain No Based on the Jarque Bera statistic it is skewed enough and kurtotic enough to be significantly non normal but only at the 1 level It is not wildly non normal d What is the central tendency of rent per person Based on the mean about 138 based in the median about 140 per month Dec 9 2003 ECON 240A 2 Final L Phillips Fig 1 2 Regression of Monthly Rent Per Person Against Persons 300 y 11 066x 165 14 R2 0 0959 Rent Per Person 250 200 150 100 50 0 0 1 2 3 4 5 6 7 Persons Living Together e Is this bivariate regression significant at the 5 level Explain No Based on an F statistic of F1 30 R2 1 R2 n 2 1 0 0959 0 9041 30 3 18 with a critical value of 4 18 at the 5 level 2 Another analyst looked at the data and noticed that rent appeared to be higher for women than for men There were 10 women in the sample and 22 men The mean rent per person for women was 164 17 and the mean rent for men was 126 35 This analyst was a student of econometrics and calculated an indicator variable for males as one minus the indicator variable for females and regressed the 32 observations for rent per person against these two indicator variables The results are displayed in Table 2 1 Then the analyst ran another regression dropping the male indicator variable and adding a constant term The results are presented in Table 2 2 Table 2 1 Regression of Rent Per Person Against Gender Indicator Variables Dependent Variable RENTPERPERSON Method Least Squares Sample 1 32 Included observations 32 Variable Coefficient Std Error t Statistic Prob FEMALE MALE 164 1667 126 3523 14 02177 9 453475 11 70799 13 36570 0 0000 0 0000 R squared Adjusted R squared S E of regression Sum squared resid Log likelihood 0 142860 0 114289 44 34073 58983 00 165 7143 Mean dependent var S D dependent var Akaike info criterion Schwarz criterion Durbin Watson stat 138 1693 47 11474 10 48215 10 57375 2 522594 Dec 9 2003 ECON 240A 3 Final L Phillips Table 2 2 Regression of Rent per Person Against the Female Indicaor Variable and a Constant Term Dependent Variable RENTPERPERSON Method Least Squares Sample 1 32 Included observations 32 Variable Coefficient Std Error t Statistic Prob FEMALE C 37 81439 126 3523 16 91089 9 453475 2 236097 13 36570 0 0329 0 0000 R squared Adjusted R squared S E of regression Sum squared resid Log likelihood Durbin Watson stat 0 142860 0 114289 44 34073 58983 00 165 7143 2 522594 Mean dependent var S D dependent var Akaike info criterion Schwarz criterion F statistic Prob F statistic 138 1693 47 11474 10 48215 10 57375 5 000131 0 032934 a Is there a significant difference in monthly rent for men and women Explain Yes The t statistic of 2 27 for the coefficient on the female variable testing the difference in mean rents is significant at the 5 level b Suppose you were not a student of econometrics and did not know about running regressions to answer this question Could you get a back of theenvelope estimate Hint Assume the square root of the estimate of the pooled variance estimator sp2 is equal to the standard deviation estimate in Figure 1 1 What do you calculate for a t statistic using this approximation t x1 x 2 1 2 0 s 1 n1 1 n 2 37 82 0 47 11 1 10 1 22 1 2 2 10 3 Someone looking at questions 1 and 2 above might wonder about combining the two analyses and regressing rent per person against both the number of persons living together and gender In the following multivariate regression rent per person was regressed against the number of persons living together the number of rooms rented the number of blocks from the center of campus and the indicator variable female The results follow in Table 3 1 a Is the regression in Table 3 1 significant as a whole at the 5 level Explain Yes the F stat of 4 27 is significant at the 1 level b Is the indicator variable female significant at the 5 level No the t stat of 1 51 is not significant at the 5 level c How can the indicator variable female be significant in Table 2 2 but not significant in Table 3 1 Explain Female was the only regressor in Table 2 2 but is one of four regressors in Table 3 1 so in the latter case the question is Dec 9 2003 ECON 240A 4 Final L Phillips whether gender is significant controlling for conditional on other factors such as rooms persons and blocks Based on the regression results in Table 3 1 two variables female and blocks were dropped although both had t statistics that were greater than one but not very significant The results are reported in Table 3 2 Table 3 1 Multivariat Regression for Rent Per Person Dependent Variable RENTPERPERSON Method Least Squares Sample 1 32 Included observations 32 Variable Coefficient Std Error t Statistic Prob ROOMS PERSONS BLOCKS FEMALE C 32 54048 39 96653 0 607752 24 87735 165 6059 13 33490 12 90240 0 578149 16 49201 17 72424 2 440249 3 097605 1 051202 1 508449 9 343470 0 0215 0 0045 0 3025 0 1431 0 0000 R squared Adjusted R squared S E of regression Sum squared resid Log likelihood Durbin Watson stat 0 387446 0 296697 39 51192 42152 17 160 3389 2 300739 Mean dependent var S D dependent var Akaike info criterion Schwarz criterion F statistic Prob F statistic 138 1693 …
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