Hand-in assignment 4 consists of
You must use this template to hand in your assignment.
Follow the following steps:
Change your name and SFU ID in the header above (between the —- and —- at the top of the file.)
Run the code in “Data Loading” below, and make sure that the data is loaded.
Add your answers under the “Answer” headings below, adding code and text to the existing sections.
Generate an .html file using Ctrl+Shft+K or by clicking “Knit”, then “Knit to HTML”.
Upload the .Rmd and .html file to Canvas.
Before you start with the questions, we start by loading the data.
Make sure that the data set “birthweight_smoking.dta” is available in the same directory where you stored this .Rmd file. The data is available from http://wps.aw.com/aw_stock_ie_3/178/45691/11696965.cw/index.html). Find “Birthweight_Smoking (E5.3, E6.1, E7.1, E9.2)”, and download the “Stata” file.
First, install the “haven” package for loading Stata files by running the following code. If you already have that data set, nothing will happen.
Now load the haven software, and store the Stata file in a data frame called “smoking”
require(foreign)## Loading required package: foreignsmoking<-read.dta("C:/Users/yuanmany/Downloads/birthweight_smoking.dta")
smoking## nprevist alcohol tripre1 tripre2 tripre3 tripre0 birthweight smoker
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## 3000 0 14 23 0The code above should have produced a data set in “smoking”. If that works, you can proceed by answering the questions below. If you have difficulties with loading the data, go to the computer lab for assistance.
Regress Birthweight on Smoker. What is the estimated effect of smoking on birth weight?
reg=lm(birthweight~smoker,data=smoking)
summary(reg)##
## Call:
## lm(formula = birthweight ~ smoker, data = smoking)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3007.06 -313.06 26.94 366.94 2322.94
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3432.06 11.87 289.115 <2e-16 ***
## smoker -253.23 26.95 -9.396 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 583.7 on 2998 degrees of freedom
## Multiple R-squared: 0.0286, Adjusted R-squared: 0.02828
## F-statistic: 88.28 on 1 and 2998 DF, p-value: < 2.2e-16We can see the coefficient of smoker is -253.23, that means if the mother smokes during pregnancy, it will cause a result that the infant birthweight decrease by 253.23.
…
Regress Birthweight on Smoker, Alcohol, and Nprevist.
reglinda=lm(birthweight~smoker+alcohol+nprevist,data=smoking)
summary(reglinda)##
## Call:
## lm(formula = birthweight ~ smoker + alcohol + nprevist, data = smoking)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2733.53 -307.57 21.42 358.09 2192.70
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3051.249 34.016 89.701 < 2e-16 ***
## smoker -217.580 26.680 -8.155 5.07e-16 ***
## alcohol -30.491 76.234 -0.400 0.689
## nprevist 34.070 2.855 11.933 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 570.5 on 2996 degrees of freedom
## Multiple R-squared: 0.07285, Adjusted R-squared: 0.07192
## F-statistic: 78.47 on 3 and 2996 DF, p-value: < 2.2e-16Using the two conditions in Key Concept 6.1, explain why the conclusion of Alcohol and Nprevist could lead to omitted variable bias in the regression estimated in (a).
The two conditions in KEY CONCEPT 6.1 states: First, the X is correlated with omitted variable. Second, the omitted variable is a determinant of the dependent variable, Y. According to this regression, alcohol, and Nprevist is determinants for birth weight of the child. Therefore, in part (a), we did not include those variables, yet they are determinant of birthweight, so part (a) regression suffers from omitted variable bias. …
Is the estimated effect of smoking on birth weight substantially different from the regression that excludes Alcohol and Nprevist? Does the regression in (a) seem to suffer from omitted variable bias?
Yes, there is a difference in the effect of smoking on birthweight, in part (a), smoking’s effect on birthweight is -253.23, but in part (b), smoking’s effect on birthweight is -217.58. Therefore, the difference in part (a) and (b) is due to omitted variable bias. …
Jane smoked during her pregnancy, did not drink alcohol, and had 8 prenatal care visits. Use the regression to predict the birth weight of Jane’s child.
The birthweight=3051.249-217.58smoking-30.491alcohol+34.070nprevist. The birthweight=3051.249-217.581+34.070*8=3106.229 gram …
Compute R2 and adjusted R2. Why are they so similar?
R2 is 0.07285; adjusted R2 is 0.07192. They are similar because both indicators measure the fraction of the sample variance of birthweight explained by the regressors, measurement of the fitness of the regression line. Adjusted R2 is just a modified version of the R2 that does not necessarily increase when a new regressor is added.
…
An alternative way to control for prenatal visits is to use the binary variables Tripre0 through Tripre3. Regress Birthweight on Smoker, Alcohol, Tripre0, Tripre2, and Tripre3.
Run this regression in the following code chunk.
regmay=lm(birthweight~smoker+alcohol+tripre0+tripre2+tripre3,data=smoking)
summary(regmay)##
## Call:
## lm(formula = birthweight ~ smoker + alcohol + tripre0 + tripre2 +
## tripre3, data = smoking)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3029.55 -307.55 31.35 372.45 2401.29
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3454.55 12.65 273.077 < 2e-16 ***
## smoker -228.85 27.16 -8.424 < 2e-16 ***
## alcohol -15.10 77.54 -0.195 0.845613
## tripre0 -697.97 106.88 -6.531 7.66e-11 ***
## tripre2 -100.84 29.62 -3.404 0.000672 ***
## tripre3 -136.96 59.58 -2.299 0.021595 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 578.7 on 2994 degrees of freedom
## Multiple R-squared: 0.04647, Adjusted R-squared: 0.04487
## F-statistic: 29.18 on 5 and 2994 DF, p-value: < 2.2e-16Why is Tripre1 excluded from the regression? What would happen if you included it in the regression?
Excluding tripre 1 because it can avoid perfect multicollinearity, since if tripre 0, tripre 2, and tripre3 are 0, then it automatically means tripre 1=1, if we include tripe 1, we would run into perfect multicollinearity, where one of the regressors is a perfect linear function of the other regressors. …
The estimated coefficient on Tripre0 is large and negative. What does this coefficient measure? Interpret its value.
The -697.97 is the coefficient on tripre0, it means that if the mother does not have any prenatal visits, the birthweight of her child will be 697.97 gram less than if she had any prenatal visits. …
Interpret the value of the estimated coefficients on Tripre2 and Tripre3.
The Tripre 2 coefficient is -100.84, it means if the mother had her 1st prenatal care in 2nd trimester, her baby’s weight will be 100.84 gram less. Also, the Tripre 3 coefficient is -136.96, it means if the mother had her 1st prenatal care in 3rd trimester, her baby’s weight will be 136.96 gram less. …
Does the regression in (d) explain a larger fraction of the variance in birthweight than the regression in (b)?
No, the part (b) regression explains a larger fraction of the variance in birthweight than part d regression, since the part (b) regression has a higher adjusted R2 of 0.07192 …
Before you start with (a)
Run three regressions:
First: (1) Birthweight on Smoker
regsmoker=lm(birthweight~smoker,data=smoking)
summary(regsmoker)##
## Call:
## lm(formula = birthweight ~ smoker, data = smoking)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3007.06 -313.06 26.94 366.94 2322.94
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3432.06 11.87 289.115 <2e-16 ***
## smoker -253.23 26.95 -9.396 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 583.7 on 2998 degrees of freedom
## Multiple R-squared: 0.0286, Adjusted R-squared: 0.02828
## F-statistic: 88.28 on 1 and 2998 DF, p-value: < 2.2e-16Then: (2) Birthweight on Smoker,Alcohol, and Nprevist
regsan=lm(birthweight~smoker+alcohol+nprevist,data=smoking)
summary(regsan)##
## Call:
## lm(formula = birthweight ~ smoker + alcohol + nprevist, data = smoking)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2733.53 -307.57 21.42 358.09 2192.70
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3051.249 34.016 89.701 < 2e-16 ***
## smoker -217.580 26.680 -8.155 5.07e-16 ***
## alcohol -30.491 76.234 -0.400 0.689
## nprevist 34.070 2.855 11.933 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 570.5 on 2996 degrees of freedom
## Multiple R-squared: 0.07285, Adjusted R-squared: 0.07192
## F-statistic: 78.47 on 3 and 2996 DF, p-value: < 2.2e-16Finally: (3) Birthweight on Smoker,Alcohol, Nprevist and Unmarried
reglisa=lm(birthweight~smoker+alcohol+nprevist+unmarried,data=smoking)
summary(reglisa)##
## Call:
## lm(formula = birthweight ~ smoker + alcohol + nprevist + unmarried,
## data = smoking)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2798.81 -309.22 25.37 361.80 2363.70
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3134.400 35.656 87.907 < 2e-16 ***
## smoker -175.377 27.099 -6.472 1.13e-10 ***
## alcohol -21.083 75.607 -0.279 0.78
## nprevist 29.603 2.898 10.213 < 2e-16 ***
## unmarried -187.133 26.007 -7.195 7.84e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 565.7 on 2995 degrees of freedom
## Multiple R-squared: 0.08861, Adjusted R-squared: 0.08739
## F-statistic: 72.79 on 4 and 2995 DF, p-value: < 2.2e-16What is the value of the estimated effect of smoking on birth weight in each of the regressions?
In 1st case, the effect of smoking on birthweight is -253.23 In 2nd case, the effect of smoking on birthweight is -217.58 In 3rd case, the effect of smoking on birthweight is -175.377 …
Construct a 95% confidence interval for the effect of smoking on birth weight, using each of the regressions.
confint(regsmoker,"smoker",level=0.95)## 2.5 % 97.5 %
## smoker -306.0736 -200.3831confint(regsan,"smoker",level=0.95)## 2.5 % 97.5 %
## smoker -269.8923 -165.2679confint(reglisa,"smoker",level=0.95)## 2.5 % 97.5 %
## smoker -228.5109 -122.2429In 1st regression, the 95% confidence interval of smoking’s effect on birthweight is{-306.0736,-200.3831} In 2nd regression, the 95% confidence interval of smoking’s effect on birthweight is {-269.8923,-165.2679} In 3rd regression, the 95% confidence interval of smoking’s effect on birthweight is{-228.5109,-122.2429}
…
Does the coefficient on Smoker in regression (1) suffer from omitted variable bias? Explain.
Yes, it suffers from omitted variable bias, since alcohol, and nprevist are determinants of birthweight, and yet they are not included in the 1st regression, so the coefficient on smoker suffer from omitted variable bias. …
Does the coefficient on Smoker in regression (2) suffer from omitted variable bias? Explain.
Yes, it suffers from omitted variable bias, as unmarried is a determinant of birthweight, and it is not included in the 2nd regression. Therefore, the coefficient on smoker suffers from omitted variable bias. …
This question is about the coeffcient on Unmarried in regression (3).
Construct a 95% confidence interval for the coefficient.
confint(reglisa,"unmarried",level=0.95)## 2.5 % 97.5 %
## unmarried -238.1276 -136.1389The 95% confidence interval of unmarried coefficient is {-238.1276,-136.1389} …
Is the coefficient statistically significant? Explain.
Yes, the coefficient of unmarried is statistically significant because the 95% confidence interval contains the estimated coefficient of unmarried of -187.133 …
Is the magnitude of the coefficient large? Explain.
Yes, the magnitude of the coefficient of unmarried is large, since it has a large value coefficient, which affects birthweight significantly. By theory, marriage should have significant impact on birthweight. Since in most cases, the only married woman would undergo proper birth preparation in marriage, where unmarried woman usually have an unexpected pregnancy, less prepared. …
A family advocacy group notes that the large coefficient suggest that public policies that encourage marriage will lead, on average, to healthier babies. Do you agree?
By looking at the coefficient of unmarried, which is -187.133, that means if the woman is unmarried, her baby will be 187.133 gram less than married woman’s baby. And by conducting the t-test, we find that coefficient of unmarried is statistically significant. Therefore, we can agree that by encourage more marriage, will lead, on average, to healthier babies. …