4. Suppose that our primary interest is inβ₁,, the partial eflect of x₁ on y. We thus estimate the equation excluding x₂:

Note that the variable x₂ may or may not be correlated with x₁ . What is the effect, if any, of excluding x2 from the model on the estimatedβ₁Explain.

 1. Explain how and why we could claim that the probability is , where Z is a standard normal random variable.

2. Is G an unbiased estimator of γ? Explain.

3. Is G a consistent cstimator ofγ? Explain.

5. Suppose we specify the model asHowever, x3 has no effect on y after x1 and x2 have been controlled for. Because we do not know thatβ3 = 0 in practice, we still estimate the equation including x3:  Notc that the variable x3 may or may not be correlated with x1 or x2. What is the effect, if any, of including x3 in the model on the estimated β1? Explain.

Question IV (48 points, 6 points each) A problem of interest to health officials is to determine the effects of smoking during pregnancy on infant health. One measure of infant health is birth weight; a birth weight that is too low can put an infant at risk for contracting various ilinesses. Our data sct contains data on births to women in the United States. Two variables of interest are the dependent variable, infant birth weight in grams (bwght), and qan explanatory variable, average numbet of cigarettes the motber smoked per day during pregnancy (cigs). We also take other factors into accoun unt and specify the model as where The estimates of this equation, obtained using the method of ordinary least squares (OLS), are given in column (1) of Table 1. Standard errors are listed in parentheses. 6. Interpret the coefficient on cigs. In particular, what is the effect on bught from smoking 10 more cigarettes per day?

7. We would like to estimate the partial effect of npvis on In(bwghr). However, we want a single value to describe this relationship. One intuitively appealing measure is the average partial efiect (APE). After computing the partial eflect and plugging in the estimated parameters, we average the partial effects for each unit across the sample. Suppose that the sample average of npvis is 11.62. What is the APE of npvis on In(bwght)?

8. Is cigs statistically significant at the 5% level against a two-sided alternative? Construct the hypotheses test in detail. Note that prob(T > 1.96) = 0.025 and prob(T > 1.645) = 0.05, where prob(T >T tc) is the area to the right of to in a t distribution with a large enough degrec of freedom.

9. Would you say that all the independent variables explain a lot of the variation in birth weight? Explain.

10. What will be the coefficients and standard errors on packs and on mage, respectively?

11. Instead of replacing cigs with packs, we add packs to the equation. What is the effect on the coefficients on cigs and packs if we include both cigs and packs in the same equation? Explain.

110年 - 110 國立臺灣大學_碩士班招生考試_國際企業研究所乙組:統計學(K)#105685

109年 - 109 國立臺灣大學_碩士班招生考試_國際企業研究所甲、乙組:統計學(G)#111284