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Using census data for the 50 U

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Using census data for the 50 U.S. states the following model was estimated (values in parentheses are the standard errors). PC = -0.365 -0.0009D +0.0094NW+0.0003 Y -0.099U + 1.519COP -0.0068AGEI +0.0077AGE2 (0.978) (0.0006) (0.0104) (0.0001) (0.084) (0.276) (0.00034) (0.0038) R-0.557 R? -0.484 ESS - 33.41 where PC - property crime index D-population density NW = percent of non-white population. Y-per-capita income in dollars U - unemployment rate COP = size of police force per thousand population AGEI = Population (in thousands) in the age group 15-24 AGE2 - Population (in thousands) in the age group 25-34 a) What signs would you expect a priori and why? Does any results surprise you? b) Test each coefficient for statistical significance at 5% level. A second model was estimated and the following results are given; (R) PC = -0.37 -0.0002Y+1.428COP -0.0068AGEI +0.0077AGE2 (0.84) (0.00008) (0.266) (0.839) (0.839) R=0.512 R? -0.468 ESS = 36.85 c) Using both the models (U) and (R), perform an appropriate test at %5 level. Be sure to state (1) the null and alternative hypotheses, (2) the statistical distribution (including the degree of freedom), and (3) the test creation for rejection of the null. What do you conclude from your test? d) For model (R), the F-statistic for overall goodness of fit is 11.8 and the corresponding p-value is 0.003. State the null hypotheses for this F-test. From the p-value would you accept or reject the null? Why? e) In Model (R), do the signs of coefficients agree with your intuition? Based on that would you say that the models here are sensible?