Using the 2012 Smoking and Drug Use Amongst English Pupils Dataset (2012smokedrugs.dta), perform diagnostics on the second cigarette consumption multiple linear regression model. To remind you, the outcome variable was cigs7, but recoded to remove all 0s, and the predictor variables were free, schyear, and sex.
Functional Form Diagnostics:
(a) Create a plot to check for a functional form violation.
(b) Perform a Ramsey RESET test.
(c) If you violate the functional form assumption, try to find a solution.
Read-in 2012 Smoking and Drug Use Amongst English Pupils, and re-run regression.
setwd("C:/QSSD/Exercises/Chapter 12 - Exercises")
getwd()
[1] "C:/QSSD/Exercises/Chapter 12 - Exercises"
library(foreign)
drugs <- read.dta("2012smokedrugs.dta", convert.factors=FALSE)
library(car)
Loading required package: carData
drugs$cigs7a <- recode(drugs$cigs7, "0=NA")
table(drugs$cigs7a)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
54 28 22 28 12 16 16 4 7 8 7 6 5 8 1 5 6 5
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
3 2 3 3 2 2 4 4 2 5 4 2 6 1 1 3 9 3
37 38 39 40 41 42 43 45 46 47 49 50 51 52 53 54 55 56
3 2 1 4 2 6 2 3 4 1 3 3 2 4 4 1 1 2
60 62 63 66 67 69 70 71 73 74 75 76 77 79 80 83 84 85
7 2 1 2 2 3 10 1 1 1 3 1 1 1 8 1 1 1
86 89 90 92 95 100 104 105 110 140
2 1 4 1 1 2 1 3 3 2
model.1 <- lm(cigs7a ~ free + schyear + sex, data=drugs)
summary(model.1)
Call:
lm(formula = cigs7a ~ free + schyear + sex, data = drugs)
Residuals:
Min 1Q Median 3Q Max
-33.31 -20.80 -12.47 15.99 122.04
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 6.549 7.452 0.879 0.3800
free 5.940 3.365 1.765 0.0783 .
schyear 3.803 1.625 2.340 0.0197 *
sex 2.811 2.855 0.984 0.3255
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 28.7 on 404 degrees of freedom
(7181 observations deleted due to missingness)
Multiple R-squared: 0.01964, Adjusted R-squared: 0.01236
F-statistic: 2.698 on 3 and 404 DF, p-value: 0.04555
Note: the general problem with regression diagnostics here is that 2 predictors are nominal and one is ordinal.
a.
x11()
plot(y=model.1$residuals,x=model.1$fitted.values, xlab="Fitted Values", ylab="Residuals")
abline(h=0, col="red")
It is not clear whether there is a local mean of 0.
b.
library(lmtest)
Loading required package: zoo
Attaching package: 'zoo'
The following objects are masked from 'package:base':
as.Date, as.Date.numeric
resettest(model.1, power=2:3, type="fitted")
RESET test
data: model.1
RESET = 0.76745, df1 = 2, df2 = 402, p-value = 0.4649
The p-value is above .05, thus we do not violate the functional form assumption.
c. Since we do not have an incorrect functional form, we do not need to attempt any corrections.
d.
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