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4 The data set BWGHT contains data on births to women in the United States. 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 regres- sion was estimated using data on n = 1,388 births: bwght = 119.77 – 0.514 cigs| (i) What is the predicted birth weight when cigs = 0? What about when cigs = 20 (one pack per day)? Comment on the difference. (ii) Does this simple regression necessarily capture a causal relationship between the child's birth weight and the mother's smoking habits? Explain. (iii) To predict a birth weight of 125 ounces, what would cigs have to be? Comment. (iv) The proportion of women in the sample who do not smoke while pregnant is about .85. Does this help reconcile your finding from part (iii)?

4 The data set BWGHT contains data on births to women in the United States. 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 regres- sion was estimated using data on n = 1,388 births: bwght = 119.77 – 0.514 cigs| (i) What is the predicted birth weight when cigs = 0? What about when cigs = 20 (one pack per day)? Comment on the difference. (ii) Does this simple regression necessarily capture a causal relationship between the child's birth weight and the mother's smoking habits? Explain. (iii) To predict a birth weight of 125 ounces, what would cigs have to be? Comment. (iv) The proportion of women in the sample who do not smoke while pregnant is about .85. Does this help reconcile your finding from part (iii)?

Linear Algebra: A Modern Introduction
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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4 The data set BWGHT contains data on births to women in the United States. 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 regres- sion was estimated using data on n = 1,388 births: bwght = 119.77 – 0.514 cigs| (i) What is the predicted birth weight when cigs = 0? What about when cigs = 20 (one pack per day)? Comment on the difference. (ii) Does this simple regression necessarily capture a causal relationship between the child's birth weight and the mother's smoking habits? Explain.
Transcribed Image Text:4 The data set BWGHT contains data on births to women in the United States. 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 regres- sion was estimated using data on n = 1,388 births: bwght = 119.77 – 0.514 cigs| (i) What is the predicted birth weight when cigs = 0? What about when cigs = 20 (one pack per day)? Comment on the difference. (ii) Does this simple regression necessarily capture a causal relationship between the child's birth weight and the mother's smoking habits? Explain.
(iii) To predict a birth weight of 125 ounces, what would cigs have to be? Comment. (iv) The proportion of women in the sample who do not smoke while pregnant is about .85. Does this help reconcile your finding from part (iii)?
Transcribed Image Text:(iii) To predict a birth weight of 125 ounces, what would cigs have to be? Comment. (iv) The proportion of women in the sample who do not smoke while pregnant is about .85. Does this help reconcile your finding from part (iii)?
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