# Does this simple regression necessarily capture a causal relationship between the child’s birth weight and the mother’s smoking habits? Explain.

**Question description**

1. These data set contains data on births to women. Two variables of interest are the dependent variable, infant birth weight in ounces (bwght), and an explanatory variable, average number of cigarettes the mother smoked per day during pregnancy(cigs). The following simple regression was estimated using data on n=1388 births:

Bwght= 119.77-0.514cigs

(1) What is the predicted birth weight when cigs = 0? What about when cigs=20(one pack per day)? Comment on the difference.

(2) Does this simple regression necessarily capture a causal relationship between the child’s birth weight and the mother’s smoking habits? Explain.

(3) To predict a birth weight of 125 ounces, What would cigs have to be?

2. List the Gauss-Markov Assumptions

3. Consider an equation to explain salaries of CEOs in terms of annual firm sales, return on equity(roe, in percentage form), return on the firm’s stock(ros, in percentage form). Through the OLS estimating, we have an equation as follows:

Log(Salary)= 4.32+0.280log(sales)+0.0174 roe +0.00024 ros (0.32) (0.035) (0.0041) (0.00054)

R2

(2) Test the null hypothesis that ros has no effect on salary against the alternative that ros has a positive effect. Carry out the test at the 10% significance level.

N=209,

=0.283

(1) Whatpercentageissalarypredictedtoincreaseifrosincreasesby50points?

1. These data set contains data on births to women. Two variables of interest

are the dependent variable, infant birth weight in ounces (bwght), and an

explanatory variable, average number of cigarettes the mother smoked per day

during pregnancy(cigs). The following simple regression was estimated using

data on n=1388 births:

Bwght= 119.77-0.514cigs

(1) What is the predicted birth weight when cigs = 0? What about when

cigs=20(one pack per day)? Comment on the difference. (2) Does this simple regression necessarily capture a causal relationship

between the child’s birth weight and the mother’s smoking habits? Explain. (3) To predict a birth weight of 125 ounces, What would cigs have to be?

2. List the Gauss-Markov Assumptions

3. Consider an equation to explain salaries of CEOs in terms of annual firm sales, return on equity(roe, in percentage form), return on the firm’s stock(ros, in

percentage form). Through the OLS estimating, we have an equation as follows:

Log(Salary)= 4.32+0.280log(sales)+0.0174 roe +0.00024 ros

(0.32) (0.035) (0.0041) (0.00054)

N=209, R

2

=0.283

(1) What percentage is salary predicted to increase if ros increases by 50 points?

(2) Test the null hypothesis that ros has no effect on salary against the alternative that ros has a

positive effect. Carry out the test at the 10% significance level.

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