(Total 20 points) You believe that the relationship between earnings and age is nonlinear. You estimate the following three polynomial regression models, controlling for the effect of gender by using a binary variable that takes on the value of one for females and is zero otherwise: Earn - 795.90 + 82.93 xAge 1.69 xAge2 +0.015 xAge3 +0.0005 xAge4 163. 19 xFemale (283.11) (29.29) (1.06) (0.016) (0.0009) (12.45) Earn = 683.21 + 65.83 xAge 1.05 xAge? +0.005 xAge 3 163.23 XFemale (120.13) (9.27) (0.22) (0.002) (12.45) Earn = - 344.88 + 41.48 xAge 0.45 xAge2 163.81 xFemale (51.58) (2.64) (0.03) (12.47) a. (5 points) Describe the general-to-specific approach to determine the appropriate degree of the polynomial using the 5% significance level. b. (3 points) Given the polynomial regression you chose in part (a), explain how you would calculate the effect of changing age by one year on earnings (holding constant the gender variable), say, age increases from x to x + 1. c. (4 points) Suppose that you decide to choose the quadratic regression above. Find the value of age that corresponds to the highest predicted valye of earnings of males. d. (4 points) Suppose that you decide to choose the quadratic regression above. Sketch the graph of fitted earnings of males against age. Does this make sense? e. (2 points) Are you concerned about the negative coefficient on the regression intercept in all the three polynomial regressions? f. (2 points) Suppose that we only consider the quadratic regression. Someone concerns the nonlinearity of not only the age variable, but also the female variable. Thus, in the quadratic regression, she adds the square term of female. That is, she is running the following regression: Earn; = Bo + B1Age + B2 Age? + B3Female; + B4Female + ui Lo + (Total 20 points) You believe that the relationship between earnings and age is nonlinear. You estimate the following three polynomial regression models, controlling for the effect of gender by using a binary variable that takes on the value of one for females and is zero otherwise: Earn - 795.90 + 82.93 xAge 1.69 xAge2 +0.015 xAge3 +0.0005 xAge4 163. 19 xFemale (283.11) (29.29) (1.06) (0.016) (0.0009) (12.45) Earn = 683.21 + 65.83 xAge 1.05 xAge? +0.005 xAge 3 163.23 XFemale (120.13) (9.27) (0.22) (0.002) (12.45) Earn = - 344.88 + 41.48 xAge 0.45 xAge2 163.81 xFemale (51.58) (2.64) (0.03) (12.47) a. (5 points) Describe the general-to-specific approach to determine the appropriate degree of the polynomial using the 5% significance level. b. (3 points) Given the polynomial regression you chose in part (a), explain how you would calculate the effect of changing age by one year on earnings (holding constant the gender variable), say, age increases from x to x + 1. c. (4 points) Suppose that you decide to choose the quadratic regression above. Find the value of age that corresponds to the highest predicted valye of earnings of males. d. (4 points) Suppose that you decide to choose the quadratic regression above. Sketch the graph of fitted earnings of males against age. Does this make sense? e. (2 points) Are you concerned about the negative coefficient on the regression intercept in all the three polynomial regressions? f. (2 points) Suppose that we only consider the quadratic regression. Someone concerns the nonlinearity of not only the age variable, but also the female variable. Thus, in the quadratic regression, she adds the square term of female. That is, she is running the following regression: Earn; = Bo + B1Age + B2 Age? + B3Female; + B4Female + ui Lo +
