Unit 7 ECONF16 (assignment answer key)

# 138 203 for the families not eligible for a 401k what

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138 203 For the families not eligible for a 401(K), what percentage of these are predicted by your model to not be eligible? For the families eligible for a 401(K), what percentage of these are predicted by your model to be eligible? What is the overall percent of observations correctly predicted by your model? 8

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For families that are not eligible, the model predicts 574/712*100 = 80.62% correct; for those families that are eligible, the model predicts 203/440*100 = 46.14% correctly. Overall, the model predicts (574 + 203)/(712 + 440). Overall the model is correct 67.45% of the time. (iii) Discuss why your work, and answers in (ii) above might be considered a better measure for the “goodness of fit” for this model rather than the traditional measure of R 2 . The R 2 for this model is actually quite low: 0.1291, and suggests not a very strong explanatory power for the “variation inY.” But with LPM models, more interesting than explaining the “variation in Y directly” is the notion of probability that Y will be 0 or 1. In this case, a more direct measure, then, of the model’s ability to predict the true value of Y would seem to be given by the analysis above. The fact that the model “predicts” the correct value for Y more than 67% of the time actually suggest the model performs pretty well, an impression that may not be had if one looked only at R 2 . 9
Software Output: #1. female 25 1 0 1 1 nonwhite 25 1 0 1 1 exper 25 16.84 11.08933 2 38 educ 25 12.28 2.47521 6 16 wage 25 4.2376 1.907481 1.96 10 Variable Obs Mean Std. Dev. Min Max -> nonwhite = 1, female = 1 female 29 0 0 0 0 nonwhite 29 1 0 1 1 exper 29 18.24138 15.57621 1 51 educ 29 11.51724 3.915361 3 18 wage 29 6.543448 3.630215 2.38 15 Variable Obs Mean Std. Dev. Min Max -> nonwhite = 1, female = 0 female 227 1 0 1 1 nonwhite 227 0 0 0 0 exper 227 16.38326 13.92611 1 50 educ 227 12.32159 2.477799 0 18 wage 227 4.626211 2.589199 .53 21.63 Variable Obs Mean Std. Dev. Min Max -> nonwhite = 0, female = 1 female 245 0 0 0 0 nonwhite 245 0 0 0 0 exper 245 17.47755 13.26667 1 49 educ 245 12.93878 2.848699 2 18 wage 245 7.165306 4.221021 1.5 24.98 Variable Obs Mean Std. Dev. Min Max -> nonwhite = 0, female = 0 . by nonwhite female, sort : summarize 10

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_cons -1.779661 .7686191 -2.32 0.021 -3.289641 -.2696803 femnon -.5810266 .8907009 -0.65 0.514 -2.330841 1.168788 nonwhite .1881548 .6095354 0.31 0.758 -1.0093 1.385609 female -2.095641 .2863739 -7.32 0.000 -2.658233 -1.533049 exper .0643575 .0104188 6.18 0.000 .0438894 .0848256 educ .6043969 .0515422 11.73 0.000 .5031403 .7056534 wage Coef. Std. Err. t P>|t| [95% Conf. Interval] Total 7160.41429 525 13.6388844 Root MSE = 3.0826 Adj R-squared = 0.3033 Residual 4941.2903 520 9.50248135 R-squared = 0.3099 Model 2219.12399 5 443.824798 Prob > F = 0.0000 F(5, 520) = 46.71 Source SS df MS Number of obs = 526 . regress wage educ exper female nonwhite femnon . generate femnon = female*nonwhite _cons -2.300828 .9085445 -2.53 0.012 -4.085688 -.5159667 femeduc -.1117433 .1001751 -1.12 0.265 -.30854 .0850535 female -.7580393 1.28162 -0.59 0.554 -3.275817 1.759739 exper .0647214 .0104068 6.22 0.000 .044277 .0851658 educ .6462078 .064354 10.04 0.000 .5197825 .772633 wage Coef. Std. Err. t P>|t| [95% Conf. Interval] Total 7160.41429 525 13.6388844 Root MSE = 3.0773 Adj R-squared = 0.3057 Residual 4933.88872 521 9.47003593 R-squared = 0.3109 Model 2226.52557 4 556.631393 Prob > F = 0.0000 F(4, 521) = 58.78 Source SS df MS Number of obs = 526 . regress wage educ exper female femeduc . generate femeduc = female*educ #2. 11
agesq 440 1785.539 833.8042 625 4096 incsq 440 2646.096 2790.387 102.5156 24523.56 pira 440 .3022727 .4597655 0 1 p401k 440 .7522727 .432184 0 1 nettfa 440 24.23968 50.59188 -502.302 398.241 fsize 440 2.920455 1.447813 1 8 age 440 41.17045 9.525678 25 64 male 440 .175 .3803996 0 1 inc 440 46.29924 22.44149 10.125 156.6 e401k 440 1 0 1 1 Variable Obs Mean Std. Dev. Min Max -> e401k = 1 agesq 712 1763.64 948.4888 625 4096 incsq 712 1464.84 2158.728 100.1601 17439.05 pira 712 .2120787 .4090676 0 1 p401k 712 0 0 0 0 nettfa 712 10.49068 35.41142 -88 397 fsize 712 2.813202 1.531735 1 9 age 712 40.55056 10.92978 25 64 male 712 .2148876 .4110331 0 1

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