1. A researcher is studying the effect of smoking on birth weight. Using data on average cigarettes smoked per day (cigs), mother's level of education (meduc), father's level of education (feduc), and logarithm of family income (1.income), the researcher estimates 3 models. Table (1) shows the OLS estimates for each model, with standard errors in parentheses underneath each coefficient. The dependent variable in all the models is birth weight. Dependent variable Independent variables Average number of cigarettes smoked per day during pregnancy by the mother (cigs) Natural logarithm of annual family income (1.income) Mother's completed years of education (meduc) Father's completed years of education (feduc) Intercept N R2 Table (1) Model 1 Birth weight (ounces) -0.47 (0.09) 116.974 (1.049) 1388 0.029 Model 2 Birth weight (ounces) -0.39 (0.09) 1.84 (0.59) 114.032 (1.946) 1388 0.030 Model 3 Birth weight (ounces) -0.35 (0.07) -0.37 (0.20) 0.41 (0.32) 115.675 (2.981) 1388 0.045 a. Interpret the R-squared of the regression in model 1. b. Test at the 5% level whether smoking has a statistically negative effect on birth weights, using the estimate in model 1. c. Carefully interpret the coefficient of income in model 2. d. The two variables that measure the effect of parental education in model 3 above are not statistically significant. Would you keep these two variables in the model? Carefully explain your answer and provide any necessary evidence to support your answer.
1. A researcher is studying the effect of smoking on birth weight. Using data on average cigarettes smoked per day (cigs), mother's level of education (meduc), father's level of education (feduc), and logarithm of family income (1.income), the researcher estimates 3 models. Table (1) shows the OLS estimates for each model, with standard errors in parentheses underneath each coefficient. The dependent variable in all the models is birth weight. Dependent variable Independent variables Average number of cigarettes smoked per day during pregnancy by the mother (cigs) Natural logarithm of annual family income (1.income) Mother's completed years of education (meduc) Father's completed years of education (feduc) Intercept N R2 Table (1) Model 1 Birth weight (ounces) -0.47 (0.09) 116.974 (1.049) 1388 0.029 Model 2 Birth weight (ounces) -0.39 (0.09) 1.84 (0.59) 114.032 (1.946) 1388 0.030 Model 3 Birth weight (ounces) -0.35 (0.07) -0.37 (0.20) 0.41 (0.32) 115.675 (2.981) 1388 0.045 a. Interpret the R-squared of the regression in model 1. b. Test at the 5% level whether smoking has a statistically negative effect on birth weights, using the estimate in model 1. c. Carefully interpret the coefficient of income in model 2. d. The two variables that measure the effect of parental education in model 3 above are not statistically significant. Would you keep these two variables in the model? Carefully explain your answer and provide any necessary evidence to support your answer.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Transcribed Image Text:1. A researcher is studying the effect of smoking on birth weight. Using data on average
cigarettes smoked per day (cigs), mother's level of education (meduc), father's level of
education (feduc), and logarithm of family income (1.income), the researcher estimates 3
models. Table (1) shows the OLS estimates for each model, with standard errors in
parentheses underneath each coefficient. The dependent variable in all the models is birth
weight.
Dependent
variable
Independent
variables
Average number of
cigarettes smoked
per day during
pregnancy by the
mother (cigs)
Natural logarithm
of annual family
income (1.income)
Mother's
completed years of
education (meduc)
Father's completed
years of education
(feduc)
Intercept
N
R2
Table (1)
Model 1
Birth weight
(ounces)
-0.47
(0.09)
116.974
(1.049)
1388
0.029
Model 2
Birth weight
(ounces)
-0.39
(0.09)
1.84
(0.59)
114.032
(1.946)
1388
0.030
Model 3
Birth weight
(ounces)
-0.35
(0.07)
-0.37
(0.20)
0.41
(0.32)
115.675
(2.981)
1388
0.045
a. Interpret the R-squared of the regression in model 1.
b. Test at the 5% level whether smoking has a statistically negative effect on birth
weights, using the estimate in model 1.
c. Carefully interpret the coefficient of income in model 2.
d. The two variables that measure the effect of parental education in model 3 above are
not statistically significant. Would you keep these two variables in the model?
Carefully explain your answer and provide any necessary evidence to support your
answer.
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