install.packages("devtools")
## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.4'
## (as 'lib' is unspecified)
install.packages("lmtest")
## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.4'
## (as 'lib' is unspecified)
install.packages("sandwich")
## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.4'
## (as 'lib' is unspecified)
library(devtools)
## Loading required package: usethis
library(lmtest)
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
library(sandwich)
devtools::install_github("JustinMShea/wooldridge")
## Skipping install of 'wooldridge' from a github remote, the SHA1 (44137328) has not changed since last install.
## Use `force = TRUE` to force installation
library(wooldridge)
data("barium")
model_barium <- lm(log(chnimp) ~ log(chempi) + log(gas) + rtwex + befile6 + affile6 + afdec6 + t, data = barium)
summary(model_barium)
##
## Call:
## lm(formula = log(chnimp) ~ log(chempi) + log(gas) + rtwex + befile6 +
## affile6 + afdec6 + t, data = barium)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.94173 -0.31037 0.03092 0.36435 1.21434
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.3972590 19.7847366 -0.121 0.90376
## log(chempi) -0.6612071 1.2224820 -0.541 0.58957
## log(gas) 0.4734524 0.8720272 0.543 0.58816
## rtwex 0.0009682 0.0044441 0.218 0.82790
## befile6 0.0878089 0.2507104 0.350 0.72676
## affile6 0.0928429 0.2572680 0.361 0.71881
## afdec6 -0.3619936 0.2907101 -1.245 0.21542
## t 0.0126198 0.0037647 3.352 0.00107 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5747 on 123 degrees of freedom
## Multiple R-squared: 0.3617, Adjusted R-squared: 0.3253
## F-statistic: 9.956 on 7 and 123 DF, p-value: 8.28e-10
model_barium_no_time <- lm(log(chnimp) ~ log(chempi) + log(gas) + rtwex + befile6 + affile6 + afdec6, data = barium)
# Perform the F-test comparing the two models
anova(model_barium, model_barium_no_time)
## Analysis of Variance Table
##
## Model 1: log(chnimp) ~ log(chempi) + log(gas) + rtwex + befile6 + affile6 +
## afdec6 + t
## Model 2: log(chnimp) ~ log(chempi) + log(gas) + rtwex + befile6 + affile6 +
## afdec6
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 123 40.631
## 2 124 44.343 -1 -3.7119 11.237 0.001066 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
model_barium_with_monthly <- lm(log(chnimp) ~ log(chempi) + log(gas) + rtwex + befile6 + affile6 + afdec6 +
feb + mar + apr + may + jun + jul + aug + sep + oct + nov + dec, data = barium)
# Display the summary of the model
summary(model_barium_with_monthly)
##
## Call:
## lm(formula = log(chnimp) ~ log(chempi) + log(gas) + rtwex + befile6 +
## affile6 + afdec6 + feb + mar + apr + may + jun + jul + aug +
## sep + oct + nov + dec, data = barium)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.99351 -0.36138 0.08331 0.41404 1.38601
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 21.149449 30.949521 0.683 0.4958
## log(chempi) 3.281504 0.491628 6.675 9.64e-10 ***
## log(gas) -1.366322 1.369156 -0.998 0.3204
## rtwex 0.006119 0.004508 1.357 0.1774
## befile6 0.145300 0.266529 0.545 0.5867
## affile6 0.015003 0.279437 0.054 0.9573
## afdec6 -0.541856 0.311689 -1.738 0.0849 .
## feb -0.427149 0.303544 -1.407 0.1621
## mar 0.058031 0.264883 0.219 0.8270
## apr -0.453006 0.268561 -1.687 0.0944 .
## may 0.035040 0.269396 0.130 0.8967
## jun -0.204567 0.269413 -0.759 0.4492
## jul 0.008259 0.278714 0.030 0.9764
## aug -0.152847 0.277969 -0.550 0.5835
## sep -0.135434 0.267967 -0.505 0.6143
## oct 0.051164 0.267134 0.192 0.8485
## nov -0.244611 0.262969 -0.930 0.3543
## dec 0.137690 0.271281 0.508 0.6128
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6016 on 113 degrees of freedom
## Multiple R-squared: 0.3576, Adjusted R-squared: 0.2609
## F-statistic: 3.7 on 17 and 113 DF, p-value: 1.351e-05
# Perform an ANOVA to compare the models
anova(model_barium_no_time, model_barium_with_monthly)
## Analysis of Variance Table
##
## Model 1: log(chnimp) ~ log(chempi) + log(gas) + rtwex + befile6 + affile6 +
## afdec6
## Model 2: log(chnimp) ~ log(chempi) + log(gas) + rtwex + befile6 + affile6 +
## afdec6 + feb + mar + apr + may + jun + jul + aug + sep +
## oct + nov + dec
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 124 44.343
## 2 113 40.892 11 3.4508 0.8669 0.5746
data("volat")
# Fit the model for the Volat dataset
model_volat <- lm(rsp500 ~ pcip + i3, data = volat)
# Display the summary of the model
summary(model_volat)
##
## Call:
## lm(formula = rsp500 ~ pcip + i3, data = volat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -157.871 -22.580 2.103 25.524 138.137
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 18.84306 3.27488 5.754 1.44e-08 ***
## pcip 0.03642 0.12940 0.281 0.7785
## i3 -1.36169 0.54072 -2.518 0.0121 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 40.13 on 554 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.01189, Adjusted R-squared: 0.008325
## F-statistic: 3.334 on 2 and 554 DF, p-value: 0.03637
summary(model_volat)$coefficients
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 18.84305624 3.2748802 5.7538154 1.444871e-08
## pcip 0.03641681 0.1293963 0.2814362 7.784810e-01
## i3 -1.36168867 0.5407244 -2.5182677 1.207402e-02
library(wooldridge)
data(barium)
str(barium)
## 'data.frame': 131 obs. of 31 variables:
## $ chnimp : num 220.5 94.8 219.4 317.4 114.6 ...
## $ bchlimp : num 9578 11219 9720 12921 9790 ...
## $ befile6 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ affile6 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ afdec6 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ befile12: int 0 0 0 0 0 0 0 0 0 0 ...
## $ affile12: int 0 0 0 0 0 0 0 0 0 0 ...
## $ afdec12 : int 0 0 0 0 0 0 0 0 0 0 ...
## $ chempi : num 100 101 101 102 104 ...
## $ gas : num 7.83e+09 8.82e+09 8.45e+09 9.24e+09 9.15e+09 ...
## $ rtwex : num 86.7 85.6 85.4 87.3 86.6 ...
## $ spr : int 0 1 1 1 0 0 0 0 0 0 ...
## $ sum : int 0 0 0 0 1 1 1 0 0 0 ...
## $ fall : int 0 0 0 0 0 0 0 1 1 1 ...
## $ lchnimp : num 5.4 4.55 5.39 5.76 4.74 ...
## $ lgas : num 22.8 22.9 22.9 22.9 22.9 ...
## $ lrtwex : num 4.46 4.45 4.45 4.47 4.46 ...
## $ lchempi : num 4.61 4.61 4.62 4.63 4.65 ...
## $ t : int 1 2 3 4 5 6 7 8 9 10 ...
## $ feb : int 1 0 0 0 0 0 0 0 0 0 ...
## $ mar : int 0 1 0 0 0 0 0 0 0 0 ...
## $ apr : int 0 0 1 0 0 0 0 0 0 0 ...
## $ may : int 0 0 0 1 0 0 0 0 0 0 ...
## $ jun : int 0 0 0 0 1 0 0 0 0 0 ...
## $ jul : int 0 0 0 0 0 1 0 0 0 0 ...
## $ aug : int 0 0 0 0 0 0 1 0 0 0 ...
## $ sep : int 0 0 0 0 0 0 0 1 0 0 ...
## $ oct : int 0 0 0 0 0 0 0 0 1 0 ...
## $ nov : int 0 0 0 0 0 0 0 0 0 1 ...
## $ dec : int 0 0 0 0 0 0 0 0 0 0 ...
## $ percchn : num 2.302 0.845 2.257 2.457 1.171 ...
## - attr(*, "time.stamp")= chr "25 Jun 2011 23:03"
barium$month <- rep(1:12, length.out = nrow(barium))
barium$month <- as.factor(barium$month)
#(i)
barium$time_trend <- 1:nrow(barium)
model_c2_1 <- lm(chnimp ~ gas + chempi + time_trend, data = barium)
summary(model_c2_1)
##
## Call:
## lm(formula = chnimp ~ gas + chempi + time_trend, data = barium)
##
## Residuals:
## Min 1Q Median 3Q Max
## -451.59 -200.59 -49.09 153.81 943.43
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.827e+01 4.659e+02 0.125 0.900673
## gas 6.686e-08 5.008e-08 1.335 0.184194
## chempi -3.739e+00 4.334e+00 -0.863 0.389901
## time_trend 6.373e+00 1.589e+00 4.012 0.000102 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 291.1 on 127 degrees of freedom
## Multiple R-squared: 0.3225, Adjusted R-squared: 0.3065
## F-statistic: 20.15 on 3 and 127 DF, p-value: 9.564e-11
model_restricted <- lm(chnimp ~ time_trend, data = barium)
model_full <- lm(chnimp ~ gas + chempi + time_trend, data = barium)
anova(model_restricted, model_full)
## Analysis of Variance Table
##
## Model 1: chnimp ~ time_trend
## Model 2: chnimp ~ gas + chempi + time_trend
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 129 10921259
## 2 127 10761080 2 160179 0.9452 0.3913
barium$month <- factor(barium$month)
model_with_dummies <- lm(chnimp ~ gas + chempi + time_trend + month, data = barium)
summary(model_with_dummies)
##
## Call:
## lm(formula = chnimp ~ gas + chempi + time_trend + month, data = barium)
##
## Residuals:
## Min 1Q Median 3Q Max
## -457.63 -224.10 -37.47 174.18 900.84
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.681e+02 4.984e+02 0.337 0.736475
## gas 3.188e-08 7.134e-08 0.447 0.655782
## chempi -2.544e+00 4.744e+00 -0.536 0.592803
## time_trend 5.942e+00 1.727e+00 3.441 0.000808 ***
## month2 1.590e+02 1.349e+02 1.179 0.240904
## month3 -1.106e+02 1.323e+02 -0.837 0.404586
## month4 1.184e+02 1.478e+02 0.801 0.424670
## month5 1.632e+01 1.463e+02 0.112 0.911363
## month6 9.568e+01 1.575e+02 0.608 0.544603
## month7 3.189e+01 1.557e+02 0.205 0.838075
## month8 1.582e+02 1.394e+02 1.134 0.259004
## month9 1.395e+02 1.411e+02 0.989 0.324782
## month10 6.595e-01 1.419e+02 0.005 0.996299
## month11 1.070e+02 1.572e+02 0.680 0.497571
## month12 1.272e+02 1.434e+02 0.887 0.376879
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 293.4 on 116 degrees of freedom
## Multiple R-squared: 0.3715, Adjusted R-squared: 0.2956
## F-statistic: 4.897 on 14 and 116 DF, p-value: 4.738e-07
data(volat)
str(volat)
## 'data.frame': 558 obs. of 17 variables:
## $ date : num 1947 1947 1947 1947 1947 ...
## $ sp500 : num 15.2 15.8 15.2 14.6 14.3 ...
## $ divyld: num 4.49 4.38 4.61 4.75 5.05 ...
## $ i3 : num 0.38 0.38 0.38 0.38 0.38 ...
## $ ip : num 22.4 22.5 22.6 22.5 22.6 ...
## $ pcsp : num NA 46.5 -48.6 -44.3 -21.4 ...
## $ rsp500: num NA 50.9 -44 -39.6 -16.3 ...
## $ pcip : num NA 5.36 5.33 -5.31 5.33 ...
## $ ci3 : num NA 0 0 0 0 ...
## $ ci3_1 : num NA NA 0 0 0 ...
## $ ci3_2 : num NA NA NA 0 0 ...
## $ pcip_1: num NA NA 5.36 5.33 -5.31 ...
## $ pcip_2: num NA NA NA 5.36 5.33 ...
## $ pcip_3: num NA NA NA NA 5.36 ...
## $ pcsp_1: num NA NA 46.5 -48.6 -44.3 ...
## $ pcsp_2: num NA NA NA 46.5 -48.6 ...
## $ pcsp_3: num NA NA NA NA 46.5 ...
## - attr(*, "time.stamp")= chr "25 Jun 2011 23:03"
model_c9 <- lm(rsp500 ~ pcip + i3, data = volat)
summary(model_c9)
##
## Call:
## lm(formula = rsp500 ~ pcip + i3, data = volat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -157.871 -22.580 2.103 25.524 138.137
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 18.84306 3.27488 5.754 1.44e-08 ***
## pcip 0.03642 0.12940 0.281 0.7785
## i3 -1.36169 0.54072 -2.518 0.0121 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 40.13 on 554 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.01189, Adjusted R-squared: 0.008325
## F-statistic: 3.334 on 2 and 554 DF, p-value: 0.03637