C2 Use the data in BARIUM for this exercise. (i) Add a linear time trend to equation (10.22). Are any variables, other than the trend, statistically significant? (ii) In the equation estimated in part (i), test for joint significance of all variables except the time trend. What do you conclude? (iii) Add monthly dummy variables to this equation and test for seasonality. Does including the monthly dummies change any other estimates or their standard errors in important ways?
#install.packages("car")
library(car)## Loading required package: carDatalibrary(wooldridge)
data<-wooldridge::barium
head(data,10)## chnimp bchlimp befile6 affile6 afdec6 befile12 affile12 afdec12 chempi
## 1 220.4620 9578.376 0 0 0 0 0 0 100.1
## 2 94.7980 11219.480 0 0 0 0 0 0 100.9
## 3 219.3575 9719.900 0 0 0 0 0 0 101.1
## 4 317.4215 12920.950 0 0 0 0 0 0 102.5
## 5 114.6390 9790.446 0 0 0 0 0 0 104.1
## 6 129.5240 11020.470 0 0 0 0 0 0 104.8
## 7 110.0920 8302.168 0 0 0 0 0 0 104.7
## 8 39.6830 9583.325 0 0 0 0 0 0 105.8
## 9 262.8230 9880.729 0 0 0 0 0 0 106.8
## 10 173.9980 9003.923 0 0 0 0 0 0 107.7
## gas rtwex spr sum fall lchnimp lgas lrtwex lchempi t feb mar
## 1 7830000128 86.74 0 0 0 5.395725 22.78123 4.462915 4.606170 1 1 0
## 2 8819999744 85.63 1 0 0 4.551748 22.90029 4.450036 4.614130 2 0 1
## 3 8449999872 85.42 1 0 0 5.390703 22.85743 4.447580 4.616110 3 0 0
## 4 9240000512 87.29 1 0 0 5.760231 22.94681 4.469236 4.629863 4 0 0
## 5 9150000128 86.60 0 1 0 4.741788 22.93702 4.461300 4.645352 5 0 0
## 6 9520000000 84.63 0 1 0 4.863866 22.97666 4.438289 4.652054 6 0 0
## 7 9770000384 82.57 0 1 0 4.701316 23.00258 4.413646 4.651099 7 0 0
## 8 9379999744 82.33 0 0 1 3.680923 22.96185 4.410736 4.661551 8 0 0
## 9 9390000128 79.45 0 0 1 5.571481 22.96291 4.375128 4.670958 9 0 0
## 10 9610000384 82.24 0 0 1 5.159044 22.98607 4.409642 4.679349 10 0 0
## apr may jun jul aug sep oct nov dec percchn
## 1 0 0 0 0 0 0 0 0 0 2.3016636
## 2 0 0 0 0 0 0 0 0 0 0.8449411
## 3 1 0 0 0 0 0 0 0 0 2.2567875
## 4 0 1 0 0 0 0 0 0 0 2.4566422
## 5 0 0 1 0 0 0 0 0 0 1.1709272
## 6 0 0 0 1 0 0 0 0 0 1.1753038
## 7 0 0 0 0 1 0 0 0 0 1.3260633
## 8 0 0 0 0 0 1 0 0 0 0.4140838
## 9 0 0 0 0 0 0 1 0 0 2.6599557
## 10 0 0 0 0 0 0 0 1 0 1.9324688#1 The coefficient is statistically significant at the 5% level. So, only Irtwex is a significant variable. The P-value of Irtwex is 0.0154, which is lower than 0.05.
attach(data)
model1<- lm(log(chnimp)~ log(chempi)+log(gas)+log(rtwex)+befile6+ affile6 +afdec6)
a <-summary(model1)
a##
## Call:
## lm(formula = log(chnimp) ~ log(chempi) + log(gas) + log(rtwex) +
## befile6 + affile6 + afdec6)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.03356 -0.39080 0.03048 0.40248 1.51720
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -17.80277 21.04537 -0.846 0.3992
## log(chempi) 3.11719 0.47920 6.505 1.72e-09 ***
## log(gas) 0.19634 0.90662 0.217 0.8289
## log(rtwex) 0.98302 0.40015 2.457 0.0154 *
## befile6 0.05957 0.26097 0.228 0.8198
## affile6 -0.03241 0.26430 -0.123 0.9026
## afdec6 -0.56524 0.28584 -1.978 0.0502 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5974 on 124 degrees of freedom
## Multiple R-squared: 0.3049, Adjusted R-squared: 0.2712
## F-statistic: 9.064 on 6 and 124 DF, p-value: 3.255e-08#2
model_2 <- lm(log(chnimp)~ log(chempi)+log(gas)+log(rtwex)+befile6+affile6+afdec6, data= data)
summary(model_2)##
## Call:
## lm(formula = log(chnimp) ~ log(chempi) + log(gas) + log(rtwex) +
## befile6 + affile6 + afdec6, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.03356 -0.39080 0.03048 0.40248 1.51720
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -17.80277 21.04537 -0.846 0.3992
## log(chempi) 3.11719 0.47920 6.505 1.72e-09 ***
## log(gas) 0.19634 0.90662 0.217 0.8289
## log(rtwex) 0.98302 0.40015 2.457 0.0154 *
## befile6 0.05957 0.26097 0.228 0.8198
## affile6 -0.03241 0.26430 -0.123 0.9026
## afdec6 -0.56524 0.28584 -1.978 0.0502 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5974 on 124 degrees of freedom
## Multiple R-squared: 0.3049, Adjusted R-squared: 0.2712
## F-statistic: 9.064 on 6 and 124 DF, p-value: 3.255e-08F= ((0.362 - 0.305)/1)/((1-0.362)/123)
F## [1] 10.98903critical_value = qf(0.95,1,123, TRUE)
critical_value## [1] 7.157589#3
model_3 <- lm(log(chnimp)~ log(chempi)+log(gas)+log(rtwex)+befile6+affile6+afdec6+feb+mar+apr+may+jun+jul+aug+sep+oct+nov+dec, data= data)
summary(model_3)##
## Call:
## lm(formula = log(chnimp) ~ log(chempi) + log(gas) + log(rtwex) +
## befile6 + affile6 + afdec6 + feb + mar + apr + may + jun +
## jul + aug + sep + oct + nov + dec, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.98535 -0.36207 0.07366 0.41786 1.37734
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 16.779215 32.428645 0.517 0.6059
## log(chempi) 3.265062 0.492930 6.624 1.24e-09 ***
## log(gas) -1.278140 1.389008 -0.920 0.3594
## log(rtwex) 0.663045 0.471304 1.407 0.1622
## befile6 0.139703 0.266808 0.524 0.6016
## affile6 0.012632 0.278687 0.045 0.9639
## afdec6 -0.521300 0.301950 -1.726 0.0870 .
## feb -0.417711 0.304444 -1.372 0.1728
## mar 0.059052 0.264731 0.223 0.8239
## apr -0.451483 0.268386 -1.682 0.0953 .
## may 0.033309 0.269242 0.124 0.9018
## jun -0.206332 0.269252 -0.766 0.4451
## jul 0.003837 0.278767 0.014 0.9890
## aug -0.157064 0.277993 -0.565 0.5732
## sep -0.134161 0.267656 -0.501 0.6172
## oct 0.051693 0.266851 0.194 0.8467
## nov -0.246260 0.262827 -0.937 0.3508
## dec 0.132838 0.271423 0.489 0.6255
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6012 on 113 degrees of freedom
## Multiple R-squared: 0.3583, Adjusted R-squared: 0.2618
## F-statistic: 3.712 on 17 and 113 DF, p-value: 1.282e-05F= ((0.358-0.305)/11)/((1-0.358)/113)
F## [1] 0.84806critical_value = qf(0.95,11,113, TRUE)
critical_value## [1] 2.041383