The following equations were estimated using the data in BWGHT.RAW: where bwght

Question

The following equations were estimated using the data in BWGHT.RAW: where bwght is the birth weight in pounds, cigs denote average number of cigarettes the mother smoked per day during pregnancy, parity is the birth order of this child, faminc denotes annual family income, motheduc denotes years of schooling for the mother, and atheduc is the number of years of schooling for the father. We have added a dummy variable for whether the child is male and a dummy variable indicating the child is classified as white. a. In the first equation, interpret the coefficient on the variable cigs. In particular, what is the effect of birth weight from smoking 10 more cigarettes per day? b. How much more is a white child predicted to weight than a nonwhite child, holding the other factors in the first equation fixed? Is the difference statistically significant? c. Comment on the estimated effect and statistical significance of motheduc. d. From the given information, why are you unable to compute the F statistic for joint significance of motheduc and fatheduc? What would you have to do to compute the statistic?

Explanation / Answer

a)The coefficient on cigs represents the difference in the predicted value of log(bwght) for each one-unit difference in cigs, if other variables remain constant. The size of the coefficient of cigs gives the size of the effect of the average number of cigarettes smoked by mother per day during pregnancy on the birth weight of the baby , and the negative sign on the coefficient says that it has a negative influence on the baby weight,i.e as the average no. of cigarettes smoked per day during pregnancy increases, the baby weight decreases.
If smoking per day increases by 10, then log(bwght) decreases by 0.052, i.e, birth weight decreases by approx. 5%. [exp(-0.052)=0.95, final value = 0.95*initial value]

b) Since race here is dummy, we know that white = 1 and non-white = 0 in the regression. Hence, keeping other factors fixed, there is an increase of 0.045 in the value of log(bwght), in case of white child than a non-white child, i.e birth weight increases for a white child by 4.6% of birth weight of a non-white child. [Same logic]
Yes, the difference is statistically significant owing to the p-value given for the coefficient (<0.05, thus significant at 5%level of significance).

c) Since the p-value for the variable 0.003<0.05, it is statistically significant at 5% level of significance( null hypothesis rejected, where the null hypothesis is coefficient is statistically insignificant).
The estimated coefficient has a negative sign implying that if motheduc increases, log(bwght) decreases, i.e with increase in years of schooling for the mother, there is a decrease in the birth weight. The coefficient -0.003 indicates that if motheduc increases by 1 year, log(bwght) decreases by 0.003, i.e if mother’s years of schooling increases by 1 year, birth weight decreases by 0.3%.

d) If our null is of the form, H0 : 1 = 2 = 0, then we can write the test statistic in the following way:
F0 =[(SSRr SSRur)/q]/[ SSRur/(n (k + 1))],
where SSRr stands for the sum of the squared residuals of the restricted model and SSRur is the same for the unrestricted model. Here,n is the number of observations, k is the number of independent variables in the unrestricted model and q is the number of restrictions (or the number of coefficients being jointly tested).
In the problem, sum of squares are not specified.

I need to know the sum of squares in order to compute the Fstatistic.

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