5. Because you know about the benefits of including control variables, you decid

Question

5. Because you know about the benefits of including control variables, you decide to add one to your study of the effect of mothers smoking on birth weight. Specifically, you think that age the mother may be related to smoking habits and birth weight. You run a multiple regression o birth weight on number of cigarettes per day and the mother's age at birth, and Stata gives of the following output: . reg birthweight number_cigarettes mon age Source df MS Number of obs 10,000 F(2, 9997) 13899.92 Model I 27160.6732 2 13580.3366 ProbF Residual 1 9767.15144 9, 997 977008247 R-squared 0.0000 0-7355 Adj R-squared 0.7355 98844 Total I 36927.8246 9,999 3.69315178 Root MSIE [95% Conf. Interval] -.2547479.2469643 mon age.1060243 .0038301-27.68 0.000-113532 -.0985166 0971468 94.63 0.000 9.002163 9.383017 birthweight 1 Coef. Std. Err. P number_cigarettes 1 - ·2508 561 .0019854-126.35 0.000 cons .19259 5a. Interpret the coefficient for number_cigarettes. How is this interpretation different from the interpretation of this coefficient in 4a? 5b. Interpret the coefficient for mom age 5c. Note the difference between the R-squared of the multiple regression model and the simple regression model. Based on this difference, which model do you think is better? Why? 5d. What do the F-statistic (F(2, 9997) and p-value for the F-statistic (Prob> F) tell you about your multiple regression model?

Explanation / Answer

Caution: Here Q4a is not given but since I can understand that 4a is of linerar regression while Q5 talks about Multi linear regression. so here below I have tried provided my answer accordingly.

5a) Co-Efficient of number of cigarets is -0.2508 which has a "-ve" sign which states that increasing the number of cigarets will result in the decrease in the birth weight of the child. So we can say that intake of 1 additional cigaret results in 0.2508 unit of birth weight reduction(considering Ceteris paribus i.e. all other things being constant). (By the same way you can compare the equation with 4a's answer as well)

5b) Just as depicted above Co-Efficient of mom age is -0.106 which has a "-ve" sign which states that increasing the mom_age will result in the decrease in the birth weight of the child. So we can say that increase of 1 unit in mom_age results in 0.106 unit of birth weight reduction(considering Ceteris paribus).

5c) Since we don't have R^2 of previous question but here we have R^2 = 0.7355 which states that 73.55% of variation in Birthweight is explained by these 2 independent variables(cigaret&mom_age). Since we need to compare the same with the previous model where we had only cigaret(i guess since you haven't provided 4a) only as the dependent variable & I believe the R^2 in the previous case might be less than 0.7355 and so we can conclude that the model in Q5 which has 2 independent variables is better model since adding more and more parametrs increase R^2 value we need to check the Adj R^2 value as well and conclude better Adj R^2 as the optimal model.

5d) The F value is the ratio of the mean regression sum of squares divided by mean error sum of squares. Its value will range from zero to an arbitrarily large number.  From F table we can get the p value which is provided below and F stat in isolation doen't mean anything. The only thing which we can say that higher the F stat lesser the p value and more and more significat the regression analysis' dependent variables.

while The value of Prob(F) is the probability that the null hypothesis for the full model is true.Since here we have (P>F) = 0 we can say that we are rejecting th null hypothesis which states that there is no relation between the dependent variables and the independent variable. And so we can conclude that there is a rellation ship existing between the independent variables(mom age & cigaret) and the dependent variable(Birthweight).

Hope the above ans has helped you in understanding the problem. Pls upvote the ans if it has really helped you. Good Luck!!

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