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![3. If there are two dummy variables Female and Male, should we include both of
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- Without running any additional tests, what can you say about the joint significance of all independent variables in the model? Which statistic(s) helps you to answer this question?1. Consider the following regression model y = x3 + u. (1) Let 3 denote the Ordinary Least Squares (OLS) estimator of B. The so-called Gauss- Markov assumptions are: • MLR.1: The true model in the population is given by (1). • MLR.2: We have a random sample of n observations {(ri, Yi), i = 1, 2, .., n} following the population model in (1). .... • MLR.3: No one explanatory variable can be written as a linear combination of the remaining explanatory variables that is, there is no perfectcollinearity. • MLR.4: In the population, the error u has an expected value of zero given any values of the explanatory variables, that is Elu|x] = 0. • MLR.5: In the population, the error u has the same variance given any values of the explanatory variables, that is Var[u|x] = o? , an unknown finite, positive constant. In the following scenarios, state whether B is an unbiased and consistent estimator of 3, and provide a brief justification for your answer in each case - but no formal mathematical…RQ7. A teacher is trying to predict student test grades (Q). She believes test grades are a function of incoming GPA, hours studying, and hours spent on social media (a distraction). She runs a regression and it produces these coefficients: Variable Coefficient Intercept GPA Hours Studying Social Media 70.0 3.5 2.4 -4.0 For a given student Julian, his GPA is 2.0, he studies 4 hours for the exam, and he spends 6 hours on Facebook. Predict his exam score (round to the nearest whole number).
- Consider the population regression of log earnings [Y;, where Y,= In(Earnings,;)] against two binary variables: whether a worker is married (D₁, where D₁;= 1 if the th person is married) and the worker's gender (D2;, where D₂;= 1 if the th person is female), and the product of the two binary variables Y₁ = Po+B₁D₁+P₂D2i + P3 (D₁¡ × D₂i) + Hi- The interaction term: O A. indicates the effect of being married on log earnings. B. does not make sense since it could be zero for married males. C. allows the population effect on log earnings of being married to depend on gender. D. cannot be estimated without the presence of a continuous variable.Suppose the researcher considers the following model : Wage = Bo+B,Female + u, and runs OLS, using wage data on 250 randomly selected male workers and 280 female workers. The researcher has obtained the estimated equation as Wage = 15 (1.00) 3 Female, R = 0.05. (0.5) In the equation, Wage is measured in dollars per hour, Female is a binary variable that is equal to 1 if the person is a female and O if the person is a male. The numbers in the parentheses are the standard errors of the coefficients. Which Statement is NOT correct? The coefficient of Female, -3.00, is statistically significant at 5%. O The p-value for the test that Ho: B = 0, H : B 0 is less than 0.05. This regression may suffer omitted variable bias. R Since insignificant. is too low, the wage difference between men and women is The researcher can increase R- by including more regressors in the model.Distinguish between the R2 and the standard error of a regression. How doeach of these measures describe the fit of a regression?
- QUESTION 7 Which is NOT true about the coefficient of determination? As you add more variables, the R-square generally rises. As you add more variables, the adjusted R-square can fall. If the R-square is above 50%, the regression is considered significant. The R-square gives the percent of the variation in the dependent variable that is explained by the independent variables. The higher is the R-square, the better is the fit.A. B. Consider data on births to women in the United States. Two variables of interest are the dependent variable, infant birth weight in ounces (bwght), and an explanatory variable, average number of cigarettes the mother smoked per day during pregnancy (cigs). The following simple regression was estimated using data on n = 1,388 births: bwght = 119.772 (0.572) n = 1,388, 0.514 cigs (0.091) R² = 0.0227, where standard errors are shown in parenthesis. What percent of the variation in birth weight is explained by cigs? What is the predicted birth weight when cigs = 0? What about when cigs = 20 (one pack per day)? Comment on the difference.Consider the following regression model: wage-Bi+Bamalerpumalexedu Buedutu, where wage is the hourly wage measured in dollars: male is a dummy variable for males edu is the years of education: maleedu is the interaction of male and edu variables. The parameter estimates for B parameters are P-1.27: B1.29: Br-0,16: Be-0.82. What is the predicted marginal effect of years of education for males?
- 3. Boyoung is writing a paper about the effect of Sunday liquor sales on drunk driving. She has panel data on which states allow liquor to be sold on Sunday in which years and wishes to estimate a difference-in-differences model. She writes the following regression equation: Year DUIRate;; = atate +a? + BTreatmentt +yControl;t + Eit i Which of the following changes does Boyoung need to make? a) She should include a constant in the regression equation. b) She should not include controls because they're already accounted for by fixed effects. c) She should include a time trend instead of time-fixed effects. d) None of the above are changes she needs to make.Explain Conditional Mean Independence by considering a regression with two regressors?The OLS estimators of the coefficients in multiple regression will have omitted variable bias: a. i only if an omitted determinant of b. if an omitted variable is correlated with at least one of the regressors, even though it is not a determinant of the dependent variable. C. only if the omitted variable is not normally distributed. d. if an omitted determinant of is a continuous variable. Y; i is correlated with at least one of the regressors. e. if the degree of freedom is less than 50.
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