S. Because you know about the benefits of inclading control variables, you decid

Question

S. Because you know about the benefits of inclading control variables, you decide to add one your study of the effect of mothers smoking on birth weight Specifically, you think thu the mother may be related to smoking habits and birth weight. You un a multiple gression of birth weight on number of cigarettes per the following output day and the mother's age at birth, and Stata gives you reg birthweight n cigarettes Source 0, 000 12 9997 2 135e0·3344 Prob ) Model 1 27160 6732 Residual 1 9767.15144,997 970824 -7355 Total 36327 8246,999 3.6931579Root birthveight 1 Std. tee 5 Cont. oterve >,2547479 .. 24044) 1353209566 -er-cigarettes 1.,2soase1 .001 9854-126.35 0.00 non age -3060243 003830 -27.680 -eens i 9.19259 ·C971468 94.630.000 9.00aio ,,38301, Sa. Interpet the coeficient for mumber cigarcties How is this interpectasion different from the interpretation of this coefficient in 4a? 5b. Interpeet the coefficient for mom age Sc. Note the difference between the R-squared of the maltiple negression model and the simple regression model. Based on this difference, which model do you think is beter? Why 5d. What do the F-statistic (F(2·9997) andp-value for the F-statistic (hob > F)tell you about your multiple regression model?

Explanation / Answer

5a.

The coefficients of num_cigarettes is -0.2508

So, the birthweight is reduced by 0.2508 when the num_cigarettes is increased by 1 units, keeping the mom_age constant.
In part 4a. the interpretation of coefficients of num_cigarettes is the birtweight is reduced by 0.2793 when the num_cigarettes is increased by 1 units.
The difference is because in the example 4 model, we have not taken into account the effect of mom_age on the birthweight.

5b.
The coefficients of mom_age is -0.106

So, the birthweight is reduced by 0.106 when the mom_age is increased by 1 units, keeping the num_cigarettes constant.

5c.
R-squared of the multiple regression model is 0.7355
R-squared of the simple regression model is 0.7152
As, the R-squared of the multiple regression model is greater than the R-squared of the simple regression model , multiple regression model of example 5 is better.

5d.
P-value (0.0000) is less than the significance level (0.05) and the observed F value is high value, which shows the multiple regression is a significant model in predicting the birthweight based on variables num_cigarettes and mom_age.

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