In the multiple regression model, the assumption of no perfect collinearity is best described as: Select one: a. The explanatory variables will not be correlated at all. O b. The explanatory variables will have correlation coefficients close to one. C C. None of the explanatory variables will be an exact linear combination of the other explanatory variables. Od. The dependent variable will not be correlated with the explanatory variables.
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- How should I interpret the coefficients on a regression with a naural log of a dependent variable? Ex: Ln(wage)=B1+B2Experience+B3Male...+UiSuppose that a researcher, using wage per hour data on 250 randomly selected male workers and 280 female workers, estimates the following OLS regression wage - 12.68+2.79xMale (0.18) (0.84) R = 0.06, s-3.10 where Male is a dummy variable that takes the value 1 if the worker is male and 0 if female: s represents the standard error of the regression and in brackets homoskedastic std errors are reported. The researcher wants to find the gender pay gap as percentage bf the wagé per hour of women. According to this information the gender pay gap on average against women is approximately -22% -25% -38% O-16%13. Collinearity in a multiple regression analysis Suppose you want to examine the effects of a training program on future earnings using the following model: earn98= 4.64 +2.376train +0.371earn96 +0.366educ- 1.86 age +2.534 married (1.14) (0.43) (0.016) (0.062) (0.013) (0.4) where earn 98- 1998 earnings, in thousands of dollars train -1 if the individual participated in the training program, and =0 otherwise earn 96- 1996 earnings, in thousands of dollars educ years of education age = age, in years married-1 if the individual is married, and -0 otherwise Suppose that there is a high degree of correlation (but not perfect) between earnings in 1996, education, age, and marital status. True or False: We should be concerned about this high degree of correlation because it affects our ability to reliably estimate the impact of the training program on 1998 earnings, T. True False
- does the simple regression of log (price) on log (nox) produce an upward or a downward biased estimator of β1?How do you interpret the R-squared obtained from running this regression?In this question we look at the relation between the logarithm of weakly earnings and years of education. Using data from the national longitudinal study of youth, we find the following results for a regression of log weekly earnings and years of education, experience, experience squared and an intercept: Log (earnings) = 4.016 + 0.092 . educi + 0.079 .expei + 0.002 . experi 2 ( 0.222) ( 0.008) ( 0.025) (0.001) c). Labour economist studying the relation between education and earnings are often concerned about what they call “ability bias”. Suppose that individuals differ in ability, and that the correct specification of the regression function is one that includes ability: log ( earnings )I = β1 + β 2 ⋅ educI + β 3 ⋅ experI − β 4 ⋅ experI2 + β5 ⋅ abilityI + εI . In this regression, what do you expect the sign of β5 (the coefficient on ability) to be?
- Consider the following log-wage regression results for women (W) and men (M) where wages are predicted by schooling (S) and age (A). wW = 2.23 + 0.077Sw + 0.017Aw and wM = 2.33 + 0.0745SM + 0.026AM. Sample means for the variables by gender are: women average a logged wage of 3.90, 12.7 years of schooling, and 40.8 years-old; men average a logged wage of 4.53, 14.2 years of schooling, and 43.9 years-old. Decompose the raw difference in average logged wages using the Oaxaca-Blinder decomposition. Specifically, decompose the raw difference into the portion due to differences in schooling, differences in age, and the portion left unexplained, possibly due to gender discrimination.Find the regression equation, letting the first variable be the predictor (x) variable. Using the listed actress/actor ages in various years, find the best predicted age of the Best Actor winner given that the age of the Best Actress winner that year is 43 years. Is the result within 5 years of the actual Best Actor winner, whose age was 45 years? Best Actress 27 30 30 61 30 32 46 28 61 22 43 56 D Best Actor 42 39 38 45 51 49 59 51 38 57 45 34 Find the equation of the regression line. y = + (Round the constant to one decimal place as needed. Round the coefficient to three decimal places as needed.) The best predicted age of the Best Actor winner given that the age of the Best Actress winner that year is 43 years is years old. (Round to the nearest whole number as needed.) Is the result within 5 years of the actual Best Actor winner, whose age was 45 years? the predicted age is the actual winner's age.Oil Recovery A U.S. state's Bureau of Economic Geology published a study on the economic impact of using carbon dioxide enhanced oil recovery (EOR) technology to extract additional oil from fields that have reached the end of their conventional economic life. The following table gives the approximate number of jobs for the citizens that would be created at various levels of recovery. Percent Recovery (%) 20 40 80 100 Jobs Created (Millions) 6 6 12 18 Find the regression line. j(r) = Use the regression line to estimate the number of jobs (in millions) that would be created at a recovery level of 50%. million jobs
- Consider the following regression estimates (ID6) Source Model Residual Total wage educ exper exper2 _cons inverse u-shaped SS C. linear d. exponential 1927.87673 5232.53756 7160.41429 df -.0046123 -3.96489 642.625576 3 522 10.0240183 525 Coef. Std. Err. .5953429 .0530251 .268287 .0368969 .000822 .7521526 MS 13.6388844 Number of obs F(3, 522) Prob > F R-squared Adj R-squared Root MSE t P>|t| 0.000 11.23 7.27 0.000 -5.61 0.000 -5.27 0.000 = .4911741 .1958023 -.006227 -5.442508 = = = 526 64.11 0.0000 0.2692 0.2650 3.1661 [95% Conf. Interval] .6995118 .3407717 where wage is hourly wage in US$, educ is years of education, exper is years of work experience and exper2 is experience squared (exper* exper). According to these estimates, what is the functional form of the relationship between experience and predicted wage when we hold education constant? a. u-shaped b.i -.0029975 -2.487272Consider the following regression estimates (FN2) Linear regression belavg abvavg female married _cons b. 1 wage O C. 5 O d. 4 Robust Coef. Std. Err. 3047845 3150202 2820787 -1.063254 .0693348 -2.751963 .9686236 .2612646 6.699098 .2889831 Number of obs F(4, 1255) Prob > F R-squared Root MSE t P>|t| -3.49 0.001 0.22 0.826 -9.76 0.000 3.71 0.000 23.18 0.000 |||||||||| = = .45606 6.132155 = -1.661197 -.5486894 -3.305361 = = [95% Conf. Interval] 1,260 56.35 0.0000 0.1121 4.3987 assume that MLR 1-6 hold. In the regression above, how many coefficients (including the constant) are statistically significant at the 1% level? a. 3 -.4653108 .687359 -2.198565 1.481187 7.266042Suppose 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.