Consider the following regression model: wage-Bi+Bamale+Bimalexedu+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: B-0,16: Be0.82. What is the predicted marginal effect of years of education for males?
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- Consider the following estimated regression model relating annual salary to years of education and work experience. Estimated Salary=10,160.10+3147.75(Education)+1230.34(Experience) Suppose an employee with 8 years of education has been with the company for 20 years (note that education years are the number of years after 8th grade). According to this model, what is his estimated annual salary?Consider the following estimated regression model relating annual salary to years of education and work experience. Estimated Salary=11,681.31+3418.97(Education)+1194.78(Experience) Suppose two employees at the company have been working there for five years. One has a bachelor's degree (8 years of education) and one has a master's degree (10 years of education). How much more money would we expect the employee with a master's degree to make?The measure of standard error can also be applied to the parameter estimates resulting from linear regressions. For example, consider the following linear regression equation that describes the relationship between education and wage: WAGEi=β0+β1EDUCi+εi where WAGEi is the hourly wage of person i (i.e., any specific person) and EDUCiEDUCi is the number of years of education for that same person. The residual εiεi encompasses other factors that influence wage, and is assumed to be uncorrelated with education and have a mean of zero. Suppose that after collecting a cross-sectional data set, you run an OLS regression to obtain the following parameter estimates: WAGEi=−12.3+4.4 EDUCi If the standard error of the estimate of β1 is 1.29, then the true value of β1 lies between (2.465, 3.11, 3.755, 1.82) and (5.69, 6.98, 5.045) . As the number of observations in a data set grows, you would expect this range to (INCREASE OR DECREASE) in size.
- In the December, 1969, American Economic Review (pp. 886-896), Nathanial Leff reports thefollowing least squares regression results for a cross section study of the effect of age composition onsavings in 74 countries in 1964:log S/Y = 7.3439 + 0.1596 log Y/N + 0.0254 log G - 1.3520 log D1 - 0.3990 log D2 (R2= 0.57)log S/N = 8.7851 + 1.1486 log Y/N + 0.0265 log G - 1.3438 log D1 - 0.3966 log D2 (R2= 0.96)where S/Y = domestic savings ratio, S/N = per capita savings, Y/N = per capita income, D1 = percentage ofthe population under 15, D2 = percentage of the population over 64, and G = growth rate of per capitaincome. Are these results correct? Explain..Consider the IV regression model Yi = β0 + β1Xi + β2Wi + ui, where Xi is correlated with ui and Zi is an instrument. Suppose that the first three assumptions in Key Concept (The IV Regression Assumptions) are satisfied. Which IV assumption is not satisfied whena) Zi is independent of (Yi, Xi, Wi)?b) Zi=Wi?c) Wi is1 for all i?d) Zi=Xi?Please no written by hand solution a) Suppose in a regression of weekly salaries on years of schooling for males(m) and females(f), the following results are obtained. Wm = 50Sm and Wf = 40Sf. where Wm (Wf) denotes weekly salary and Sm (Sf) denotes years of schooling for males and females respectively. 50 and 40 are the coefficients on schooling in the male and female regression respectively. On average, men have 12 years of schooling and women have 10 years of schooling. What is the average male-female wage differential? Is this a good estimate of discrimination? Explain why/why not. Using the information in the question, what would you propose as a better estimate of discrimination? State any assumptions that you use and explain your answer.
- You estimated the following regression. What value would you predict for Y, if X = 47? (Round your final answer to zero decimal places.) Source | SS df MS Number of obs = 324 -------------+---------------------------------- F(1, 322) = 354.54 Model | 3686788 1 3686788 Prob > F = 0.0000 Residual | 3348384.74 322 10398.7104 R-squared = 0.5241 -------------+---------------------------------- Adj R-squared = 0.5226 Total | 7035172.74 323 21780.7206 Root MSE = 101.97 ------------------------------------------------------------------------------ Y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 24.51522 1.301971 18.83 0.000 21.95378 27.07666 _cons | 98.70791 117.4919 0.84 0.401…Given the regression equation Y = 100 + 10X a. What is the change in Y when X changes by +3? b. What is the change in Y when X changes by -4? c. What is the predicted value of Y when X = 12? d. What is the predicted value of Y when X = 23? e. Does this equation prove that a change in X causes a change in Y?A company wants to use regression analysis to forecast the demand for the next quarter.In such a regression model, demand would be the independent variable. True or false?a. Trueb. False
- Suppose that an economist has been able to gather data on the relationship between demand and price for a particular product. After analyzing scatterplots and using economic theory, the economist decides to estimate an equation of the form Q= aPb, where Q is quantity demanded and P is price. An appropriate regression analysis is then performed, and the estimated parameters turn out to be a = 1000 and b = - 1.3. Now consider two scenarios: (1) the price increases from $10 to $12.50; (2) the price increases from $20 to $25. a. Do you predict the percentage decrease in demand to be the same in scenario 1 as in scenario 2? Why or why not? b. What is the predicted percentage decrease in demand in scenario 1? What about scenario 2? Be as exact as possible.In general, what is true about the relationship between the Sum of Squared Residuals in the restricted and unrestricted model? a. SSRr = R-squared * SSRur b. SSRr < SSRur c. SSRr > SSRur d. SSRr = SSRurSuppose output (Q) is related to labor (L) and capital (K) in the following nonlinear way: Q = aLbKc When taking log to this equation, it is transformed into a linear LnQ = lna + b ln(L) + c Ln (K) One hundred twenty-three observations are used to obtain the following regression results: Dependant Variable: Q R-square F-ratio p-value on F Observations: 123 0.7547 184.56 0.00001 Variable Parameter Estimate Standard error t-ratio p-value Intercept 5.5215 0.9750 5.66 0.0001 L 0.650 0.2950 2.20 0.0295 K 0.350 0.1450 2.41 0.0173 A. Write the regression equation based on the output either in the transformed linear form or the original non-linear form. B. How do we interpret the coefficient of labor (L)? C. Is it statistical significance at the 1 percent level of significance?