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Homework answers / question archive / A data set of 1388 infants contains information regarding infant birth weights in grams (bwghtgrams) and the number of cigarettes per day that an infant's mother smoked during pregnancy (cigs)
A data set of 1388 infants contains information regarding infant birth weights in grams (bwghtgrams) and the number of cigarettes per day that an infant's mother smoked during pregnancy (cigs). An OLS regression of bwghtgrams on cigs is given as follows: bwghtgrams_hat=3395.48 - 14.57*cigs se: (16.23) (2.57) t-stat: (209.27) (-5.67) p-value: (0.00) (0.00) R-square - 0.023 (a) Interpret the coefficients. (b) What is the p-value of the significance test on the OL S slope parameter? Given this p-value, can we reject the null hypothesis at the 5% significance level? (c) What percentage of variation in infant's birth weight is explained by mother's smoking intensity? (d) Predict the birth weight of a baby born to a non-smoking mother. (e) How much will birth weight change if the number of cigarettes smoked changes from 0 to 10?
The expected value of the infant birth weight on an average is 3395.48 grams for a mother who smoked zero cigarettes during pregnancy.
Interpretation of the slope term:
As the cigarettes smoked increases by 1 unit the expected value of the infant birth weight on an average decreases by 14.57 grams.
Answer b: The p value of the significance of the OLS slope parameter is 0. This means that the coefficient for slope term is statistically significant at significance level of 5 percent. This is because according to the rule if the p value is less than the level of significance, we reject the null hypothesis which says the slope term is insignificant.
Answer c: Here R square represnts the percentage of variation in infants birth weight due to mother's smoking intensity. The value of r square is 0.023 which means that only 2.3 percent variation in the birth weight of the infant can be explained by the model.
Answer d: Birth weight of a baby to non smoking mother will be 3395.48 grams. We get this because the slope term becomes 0 as number of cigarettes smoked is zero.
Answer e: For this we need to find the birth weight of a baby where the mother smoked 10 cigarettes which will be:
bwtghtgrams= 3395.48-14.57×(10)= 3249.78
Now to find the weight change we subtract this value from the value of birth weight when the mother smoked zero cigarettes which will be:
