辅导 ECON 3018, Econometrics Final Exam辅导留学生Matlab语言

ECON 3018, Econometrics

Th 12/20/2012

Final Exam

1. You have been asked by your younger sister to help her with her science fair project. Having learned regression techniques recently, you suggest that she investigate the weight-height relationship of 4^th to 6^th graders. Her presentation topic will be to explain how people at carnivals predict weight by observing height. You collect data for roughly 100 boys and girls between the ages of nine and twelve and estimate for her the following relationship:

Weight = 45.59 + 4.32 × Height4, R² = 0.55, SER = 15.69

(3.81) (0.46)

where Weight is in pounds, and Height4 is inches above 4 feet.

a. Interpret the intercept.

b. Interpret the coefficient on Height4.

c. You remember from the medical literature that females in the adult population are, on average, shorter than males and, controlling for height, weigh less. You add a binary variable (DFY) that takes on the value one for girls and is zero otherwise. You estimate the following regression function:

Weight = 36.27 + 17.33 × DFY + 5.32 × Height4 – 1.83 × (DFY × Height4),

(5.99) (7.36) (0.80) (0.90)

R2 = 0.58, SER = 15.41

i. Interpret the new coefficients.

ii. Write down the regression function for boys and girls separately and then, on the axes below, sketch the regression function for boys and girls separately. Make sure your graph is clearly labeled, including the axes and intercepts.

iii. Should the weight-predictor at the carnival calculate weight from height differently for boys and girls? (Hint: Formally state a null and alternative hypothesis, and perform. the test.)

2. Consider estimating the effect of the student-to-teacher ratio (STR) on the high school graduation (GradR) for the Northeast Region of the United States (Maine, Vermont, New Hampshire, Massachusetts, Connecticut and Rhode Island) for the period 1991-2001. In your regression, STR is the only explanatory variable.

a. Write the regression equation, including state fixed effects.

b. If you wanted to control for state fixed effects using dummy variables, how many binary variables would you have to include to estimate the regression equation from part (a)? Explain your answer.

c. Give examples of some of the factors that the inclusion of state fixed effects controls for.

d. Write the regression equation, including time fixed effects (excluding state fixed effects).

e. To estimate the regression equation from part (d), how many binary variables do you have to estimate? Explain your answer.

f. Give examples of some of the factors that the inclusion of time fixed effects controls for.

3. If we suspect that the effect of X on Y depends on the level of another variable W, we can model this using an interaction term multiplying X and W. We also discussed two general modeling methods that we can we use if we suspect that the effect of X on Y depends on the level of X. Below are two incomplete regression equations, each corresponding to one of these general modeling methods. Alter only the right-hand-side of each equation to specify these methods. For each, interpret how a change in X affects Y.

Y_i = b₀ + + u_i

4. A study analyzed the probability of Major League Baseball (MLB) players to "survive" for another season, or, in other words, to play one more season. The researchers had a sample of 4,728 hitters and 3,803 pitchers for the years 1901-1999. Observations for all explanatory variables are standardized (i.e. each observation has had its mean value subtracted from it and has been divided by its standard deviation). The probit estimation yielded the results as shown in the table:

Regression	(1) Hitters	(2) Pitchers
Regression model	probit	Probit
constant	2.010 (0.030)	1.625 (0.031)
number of seasons played	-0.058 (0.004)	-0.031 (0.005)
performance	0.794 (0.025)	0.677 (0.026)
average performance	0.022 (0.033)	0.100 (0.036)

where the limited dependent variable takes on a value of one if the player had one more season (a minimum of 50 at bats or 25 innings pitched), number of seasons played is measured in years, performance is the batting average for hitters and the earned run average for pitchers, and average performance refers to performance over the career.

a. Calculate survival probabilities for hitters and pitchers at the sample mean. Are your answers higher or lower than you’d expect?

b. What are the units of the standardized explanatory variables? Given your calculation in part (a), why might the researchers have chosen to standardize the variables?

c. Calculate the change in the survival probability for a hitter who has a very bad year by performing two standard deviations below the average (assume also that this player’s number of seasons played is the mean and that this value is high enough so that his average performance is hardly affected). How does this change the survival probability when compared to the answer in (a)?

d. Repeat part (c) for a pitcher.

e. Since the results seem similar for hitters and pitchers, the researcher could consider combining the two samples. Explain in detail how this could be done and how you could test the hypothesis that the coefficients are the same.

5. Derive the ordinary least squares estimator of b₀ in the simple regression, Y_i = b₀ + b₁X_i + u_i

6. Can a regression analysis exhibit internal validity but not external validity? If yes, give an example. If not, discuss why not. Be sure to define both internal and external validity in your answer.

辅导 ECON 3018, Econometrics Final Exam辅导 留学生Matlab语言

辅导 ECON 3018, Econometrics Final Exam辅导留学生Matlab语言