Question

For a regression with log(bweight) as the dependent variable, we have

Variable	Estimate	Standard Error
Constant/Intercept	4.66	0.029
Male	0.03	0.010
Motheduc	0.002	0.002
lfaminc	0.02	0.006

You expect an increase in family income to increase birth weight. Test this hypothesis at the 1% level of significance. Make sure you explicitly include all of the steps.

Answer 1

Since the dependent variable is log(bweight), to test the hypothesis of the dependence of birth weight on financial income, first we take antilog of the estimate slope value for financial income variable(Ifaminc) and its S.E..

Therefore the corresponding values become

Estimate() = antilog(0.02)=1.047

Standard Error= antilog(0.006)=1.014

Hence for testing the hypothesis that an increase in family income increase birth weight, the null hypothesis will be

against the alternative

the test statistic would be

the corresponding critical value of t will be calculated from the given table, at 0.01 significance level in one-tail row with n-4 degrees of freedom(where n is number of observations in your data)

For example if n=20, the critical value will be 2.583. For illustration, we assume critical value as ttab

Now if ttab>1.033, we fail to reject the null hypothesis and conclude that an increase in family income does not result in an increase in birth weight and

if ttab<1.033, then we reject our null hypothesis and conclude that an increase in family income results in an increase in birth weight.