I have 4 data sets which is CO2 emission , GDP per capita, GDP per capita square and Number of tourist arrival. I am trying to run a model to observe the number of tourist arrival impact on Co2 emission in order to derive the Tourism induced Environmental Kuznets Curve. Below is the code and summary results . Without log
Yt<-Data$`CO2 emissions`
X1t<-Data$`GDP per capita`
X2t<-Data$`GDP per caita square`
X3t<-Data$`Number of Tourist arrival`
model<-lm(Yt~X1t+X2t+X3t)
summary(model)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.238e-02 7.395e-03 1.674 0.100187
X1t -2.581e-05 6.710e-05 -0.385 0.702139
X2t 1.728e-07 4.572e-08 3.780 0.000413 ***
X3t 1.928e-07 3.501e-08 5.507 1.2e-06 ***
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.02252 on 51 degrees of freedom
Multiple R-squared: 0.9475, Adjusted R-squared: 0.9444
F-statistic: 306.5 on 3 and 51 DF, p-value: < 2.2e-16
With log
LYt<-(log(Yt))
LX1t<-(log(X1t))
LX2t<-(log(X2t))
LX3t<-(log(X3t))
model1<-lm(LYt~LX1t+LX2t+LX3t)
summary(model1)
Coefficients: (1 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
(Intercept) -9.38623 0.46040 -20.387 < 2e-16 ***
LX1t 0.83679 0.09834 8.509 2.01e-11 ***
LX2t NA NA NA NA
LX3t 0.17802 0.06888 2.585 0.0126 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.2863 on 52 degrees of freedom
Multiple R-squared: 0.9074, Adjusted R-squared: 0.9038
F-statistic: 254.7 on 2 and 52 DF, p-value: < 2.2e-16
It is pretty evident that GDP per capita and GDP per capita square are perfectly collinear. However, why does the regression coefficients show missing values (NA) only in the case of log transformed model?