It seems that the variables Fertility and Education are the closest related variables.
library(psych)
cor(swiss)
## Fertility Agriculture Examination Education Catholic
## Fertility 1.0000000 0.35307918 -0.6458827 -0.66378886 0.4636847
## Agriculture 0.3530792 1.00000000 -0.6865422 -0.63952252 0.4010951
## Examination -0.6458827 -0.68654221 1.0000000 0.69841530 -0.5727418
## Education -0.6637889 -0.63952252 0.6984153 1.00000000 -0.1538589
## Catholic 0.4636847 0.40109505 -0.5727418 -0.15385892 1.0000000
## Infant.Mortality 0.4165560 -0.06085861 -0.1140216 -0.09932185 0.1754959
## Infant.Mortality
## Fertility 0.41655603
## Agriculture -0.06085861
## Examination -0.11402160
## Education -0.09932185
## Catholic 0.17549591
## Infant.Mortality 1.00000000
#We can analyze the correlations between the variables and find out which one is suitable for fertility
plot(swiss$Fertility~swiss$Education, xlab='Education', ylab='Fertility')
abline(lm(swiss$Fertility~swiss$Education))
plot(swiss$Fertility~swiss$Examination, xlab='Examination', ylab='Fertility')
abline(lm(swiss$Fertility~swiss$Examination))
sample1<-lm(Fertility~Education, data=swiss)
summary(sample1)
##
## Call:
## lm(formula = Fertility ~ Education, data = swiss)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17.036 -6.711 -1.011 9.526 19.689
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 79.6101 2.1041 37.836 < 2e-16 ***
## Education -0.8624 0.1448 -5.954 3.66e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.446 on 45 degrees of freedom
## Multiple R-squared: 0.4406, Adjusted R-squared: 0.4282
## F-statistic: 35.45 on 1 and 45 DF, p-value: 3.659e-07
sample2<-lm(Fertility~Examination, data=swiss)
summary(sample2)
##
## Call:
## lm(formula = Fertility ~ Examination, data = swiss)
##
## Residuals:
## Min 1Q Median 3Q Max
## -25.9375 -6.0044 -0.3393 7.9239 19.7399
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 86.8185 3.2576 26.651 < 2e-16 ***
## Examination -1.0113 0.1782 -5.675 9.45e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.642 on 45 degrees of freedom
## Multiple R-squared: 0.4172, Adjusted R-squared: 0.4042
## F-statistic: 32.21 on 1 and 45 DF, p-value: 9.45e-07
plot(sample1)
plot(sample2)