Question

Consider the following multiple regression results below, which examine the potential impact of smoking by the mother during pregnancy has on the birth weights of their newborns. In the models reported below, the dependent variable is birth weight (in pounds). The explanatory variables are: the number of cigarettes smoked per day during pregnancy by the mother, the birth order of the child in the family (with 1 denoted first-born, 2 second-born, etc.), the gender of the child (=1 if male and o otherwise), the race of the child (=1 if white and otherwise), family income (in dollars), the mother's years of education, and the father's years of education. Dependent Variable: Birth weight (in pounds) Estimated Coefficients with Standard Errors in Parentheses Explanatory Variables Constant Number of cigarettes Birth order Regression 1 6.814 (0.246) -0.037 (0.007) 0.120 (0.041) 0.237 (0.071) 0.295 (0.100) 0.003 (0.002) -0.021 (0.020) 0.026 (0.018) Regression 2 6.943 (0.121) -0.039 (0.007) 0.120 (0.041) 0.234 (0.071) 0.335 (0.098) Regression 3 -189.055 (229.788) 1.449 (1.646 -4.858 (5.453) -8.657 (9.740) -18.170 (20.523) Gender of child Race of child Family Income Mother's education Father's education Predicted birth weight squared (?) Predicted birth weight cubed (Y) Residual sum of squares (RSS) Number of observations 5.835 (7.194) -0.247 (0.342) 1,785.000 1,783.647 1,790.836 1191 1191 1191

Answer 1

Sol:

the test statistic is given by:

[(SSR restricted - SSR unrestricted)/number of restrictions]/[(SSR unrestricted/(n - k -1)]

= ((1790.836 - 1783.647)/3)/((1783.647)/(1191 - 7 -1))

= 1.59

Thus, the answer is (d) 1.59

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