A problem of interest to health officials (and others) is to determine the effects of smoking during pregnancy on infant health. One measure of infant health is birth weight; a birth weight that is too low can put an infant at risk for contracting various illnesses. Since factors other than cigarette smoking that affect birth weight are likely to be correlated with smoking, we should take those factors into account. For example, higher income generally results in access to better prenatal care, as well as better nutrition forthe mother. An equation that recognizes this is \(bwght = \beta_0 + \beta_1cigs + \beta_2 faminc + u.\)
\beta_2?cigs and faminc are likely to be correlated? Explain why the correlation might be positive or negative.faminc, using the data in BWGHT.RAW. Report the results in equation form, including the sample size and R-squared. Discuss your results, focusing on whether adding faminc substantially changes the estimated effect of cigs on bwght.library('wooldridge')
data('bwght')
?bwght
#1)
#likely to be positive
#2)
#Yes
#negative correlation
linearBwght0 <- lm(cigs ~ faminc, data=bwght)
summary(linearBwght0)
#3)
linearBwght1 <- lm(bwght ~ cigs + faminc, data=bwght)
linearBwght2 <- lm(bwght ~ cigs, data=bwght)
summary(linearBwght1)
summary(linearBwght2)Use the data in HPRICE1.RAW to estimate the model \(price = \beta_0 + \beta_1sqrft + \beta_2bdrms + u,\) where price is the house price measured in thousands of dollars.
sqrft = 2,438 and bdrms = 4. Find the predicted selling price for this house from the OLS regression line.price = 300). Find the residual for this house. Does it suggest that the buyer underpaid or overpaid for the house?library('wooldridge')
data('hprice1')
?hprice1
#1)
linearHprice <- lm(price ~ sqrft + bdrms, data=hprice1)
summary(linearHprice)
#2)
#+15.2 thousand dollars
#3)
140*0.128+15.2
#33.12 thousand dollars
#4)
#R2 = 0.63
#5)
2438*0.128+4*15.2-19.31
#354 thousand dollars
#6)
354-300
#residual of 54 thousand dollars
#the buyer underpaidThe file CEOSAL2.RAW contains data on 177 chief executive officers and can be used to examine the effects of firm performance on CEO salary.
ceoten to the model in question 2. What is the estimated percentage return for another year of CEO tenure, holding other factors fixed?log(mktval) and profits. Are these variables highly correlated?library('wooldridge')
data('ceosal2')
?ceosal2
#1)
linearCEO <- lm(log(salary) ~ log(sales) + log(mktval), data=ceosal2)
summary(linearCEO)
#2)
linearCEO2 <- lm(log(salary) ~ log(sales) + log(mktval) + profits, data=ceosal2)
summary(linearCEO2)
min(ceosal2$profits)
#because it contains negative values
#Yes, R2 is important
#3)
linearCEO3 <- lm(log(salary) ~ log(sales) + log(mktval) + profits + ceoten, data=ceosal2)
summary(linearCEO3)
#4)
linearCEO4 <- lm(log(mktval) ~ profits, data=ceosal2)
summary(linearCEO4)
#Yes, R2 is importantThe following model can be used to study whether campaign expenditures affect election outcomes: \(voteA = \beta_0 + \beta_1log(expendA) + \beta_2log(expendB) + \beta_3 prtystrA + u,\) where voteA is the percentage of the vote received by Candidate A, expendA and expendB are campaign expenditures by Candidates A and B, and prtystrA is a measure of party strength for Candidate A (the percentage of the most recent presidential vote that went to A’s party).
library('wooldridge')
data('vote1')
?vote1
#1)
#beta_1 measures the percentage point candidate A votes increases when candidate A expenditures increase by 100%
#2)
#H_0: \beta_1 + \beta_2 = 0
#3)
linearVote <- lm(voteA ~ log(expendA) + log(expendB) + prtystrA, data=vote1)
summary(linearVote)
#No (linear combination of two estimates)
#4)
linearVote2 <- lm(voteA ~ log(expendA) + log(expendB/expendA) + prtystrA, data=vote1)
summary(linearVote2)
#We fail to reject H_0Use the data in WAGE2.RAW for this exercise.
log(wage).log(wage) as another year of tenure with the current employer.library('wooldridge')
data('wage2')
?wage2
#1)
#H_0: \beta_2 = 0
#2)
linearWage <- lm(log(wage) ~ educ + exper + tenure, data=wage2)
summary(linearWage)
#Significant. a 1-year experience increases wage by 1.53%
#3)
#H_0: \beta_2 - \beta_3 = 0
#4)
wage_new <- wage2 %>% mutate(var=exper+tenure)
linearWage2 <- lm(log(wage) ~ educ + exper + var, data=wage_new)
summary(linearWage2)
#We fail to reject H_0The data set 401KSUBS.RAW contains information on net financial wealth nettfa, age of the survey respondent age, annual family income inc, family size fsize, and participation in certain pension plans for people in the United States. The wealth and income variables are both recorded in thousands of dollars. For this question, use only the data for single-person households (so fsize = 1).
nettfa on inc, is the estimated coefficient on inc much different from the estimate in question 2? Why or why not?library('wooldridge')
data('k401ksubs')
?k401ksubs
#1)
k401ksubs %>% filter(fsize==1) %>% summarise(n())
#2)
data_single <- k401ksubs %>% filter(fsize==1)
linear_single <- lm(nettfa ~ inc + age, data=data_single)
summary(linear_single)
#Not very surprising
#3)
#Not an interesting meaning
#4)
#Yes
#5)
simple_linear <- lm(nettfa ~ inc, data=data_single)
summary(simple_linear)
#Not so different