Smoking causes cancer, heart disease, and other major health problems. Smoking during pregnancy causes additional health problems, including premature birth (being born too early), certain birth defects, and infant death (www.cdc.gov).
The data file BWEIGHT.gdt contains 1191 observations on the following variables. The variables descriptions are as follows:
1. faminc = 1988 family income, $1000s
2. bwght = birth weight, grams
3. fatheduc = father's years of education
4. motheduc = mother's years of education
5. parity = birth order of child
6. male = =1 if male child
7. white = =1 if white
8. cigs = number of cigarettes smoked by the mother per day while pregnant
9. 1_bwght = log of birth weight
10. 1_faminc = log of family income
Model 1:
bwghti = β1 + β2cigsi + β3 faminci + β4 parityi + β5 malei + β6 whitei + ei (1)
Model 2:
l_bwghti = α1 + α2cigsi + α3 l_aminci + α4 parityi + α5 malei + α6 whitei + α7 motheduci + α8 fatheduci + ωi (2)
Assume that the random error terms follow a normal distribution with mean zero and variance σ2.
(To answer the questions regarding the hypothesis tests, you must provide the null and alternative hypotheses, test statistics, the distribution of the test statistics under the null, and the degrees of freedom, critical value(s), decision rule and your conclusion. Follow all the test steps in hypothesis testing described in the textbook chapter 3.4).
Model 1
1. Estimate Model 1 and provide a summary report (see note below). Copy and paste your Gretl regression output.
(Note: the summary report should contain the estimated regression equation, standard errors, test statistics, the number of observations, goodness of fit statistic, and the F value for the overall significance test. See the example below.
Y^ = 5.6 -0.067 X1 + 1.76 X2
se(..?..)(..?..) (..?..)
t(..?..)(..?..) (..?..)
N = ? R2 = ? F = ?
2. Discuss your summary report in terms of significance of the coefficients, R2 and overall significance of the model based on the F-statistic (no need to carry out hypothesis tests).
3. Is there evidence to suggest that smoking causes a low birth weight? Test the claim at the 1% significance level and clearly state your conclusion. Follow all the test steps in hypothesis testing.
4. Is there significant evidence that smoking 10 more cigarettes decreases birth weight by more than 100grams? Test your claim at the 5% significance level. Follow all the test steps in hypothesis testing.
5. Interpret the coefficients β5 and β6. How much more is a white child expected to weigh than a non-white child, holding other factors constant in the model? Is the difference statistically significant? Justify your answer (no need to carry out a hypothesis test).
Model 2
6. Estimate Model 2 and copy and paste your Gretl output. Is there significant evidence to show that a mother's education has a greater impact on birth weight than a fathers' education? Test your claim at the 1% significance level. Follow all the test steps in hypothesis testing.
7. Test the null hypothesis that, after controlling for cigs, parity and faminc, parents' education has no effect on birth weight. Follow all the test steps in hypothesis testing.
8. Test the overall significance of the model at the 5% significance level and comment on your results. Follow all the test steps in hypothesis testing.
9. Predict the weight for a female baby who is third in birth order, the parents have 20 years of education, wtih a family income of $15,500, and the mother smokes six cigarettes a day, on average. Calculate a 95% prediction interval and interpret your answer. Please note that the dependent variable is in logs so you need to take the antilog to change it to actual values.
10. Based on the two models which model would you prefer and why? Explain.