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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 4th to 6th 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.