library(faraway)
data(longley)
? longley
#Q1 (refer Ex0404)
#(a)
options(digits=3)
cor(longley, use = "everything", method = "pearson")
## GNP.deflator GNP Unemployed Armed.Forces Population Year
## GNP.deflator 1.000 0.992 0.621 0.465 0.979 0.991
## GNP 0.992 1.000 0.604 0.446 0.991 0.995
## Unemployed 0.621 0.604 1.000 -0.177 0.687 0.668
## Armed.Forces 0.465 0.446 -0.177 1.000 0.364 0.417
## Population 0.979 0.991 0.687 0.364 1.000 0.994
## Year 0.991 0.995 0.668 0.417 0.994 1.000
## Employed 0.971 0.984 0.502 0.457 0.960 0.971
## Employed
## GNP.deflator 0.971
## GNP 0.984
## Unemployed 0.502
## Armed.Forces 0.457
## Population 0.960
## Year 0.971
## Employed 1.000
#(b) either command can be used
plot(longley)
pairs(longley)
#(c) (refer pg4)
fit = lm(Employed ~ GNP.deflator+GNP+Unemployed+Armed.Forces+Year+Population, data = longley)
summary(fit)
##
## Call:
## lm(formula = Employed ~ GNP.deflator + GNP + Unemployed + Armed.Forces +
## Year + Population, data = longley)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.4101 -0.1577 -0.0282 0.1016 0.4554
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.48e+03 8.90e+02 -3.91 0.00356 **
## GNP.deflator 1.51e-02 8.49e-02 0.18 0.86314
## GNP -3.58e-02 3.35e-02 -1.07 0.31268
## Unemployed -2.02e-02 4.88e-03 -4.14 0.00254 **
## Armed.Forces -1.03e-02 2.14e-03 -4.82 0.00094 ***
## Year 1.83e+00 4.55e-01 4.02 0.00304 **
## Population -5.11e-02 2.26e-01 -0.23 0.82621
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.305 on 9 degrees of freedom
## Multiple R-squared: 0.995, Adjusted R-squared: 0.992
## F-statistic: 330 on 6 and 9 DF, p-value: 4.98e-10
vif(fit)
## GNP.deflator GNP Unemployed Armed.Forces Year
## 135.53 1788.51 33.62 3.59 758.98
## Population
## 399.15
#(d) (refer pg6)
fit2 = lm(Population ~ GNP.deflator+GNP+Unemployed+Armed.Forces+Year, data = longley)
fit3 = lm(Employed ~ GNP.deflator+GNP+Unemployed+Armed.Forces+Year, data = longley)
cor(fit2$residuals,fit3$residuals)
## [1] -0.0751
plot(fit2$residuals,fit3$residuals)
abline(h=0,lty=2)
abline(v=0,lty=2)
abline(lm(fit3$residuals ~ fit2$residuals))
#(e) (refer pg6)
fit4 = lm(Employed ~ Unemployed+Armed.Forces+Year, data = longley)
summary(fit4)
##
## Call:
## lm(formula = Employed ~ Unemployed + Armed.Forces + Year, data = longley)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.5729 -0.1199 0.0409 0.1398 0.7530
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.80e+03 6.86e+01 -26.18 5.9e-12 ***
## Unemployed -1.47e-02 1.67e-03 -8.79 1.4e-06 ***
## Armed.Forces -7.72e-03 1.84e-03 -4.20 0.0012 **
## Year 9.56e-01 3.55e-02 26.92 4.2e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.332 on 12 degrees of freedom
## Multiple R-squared: 0.993, Adjusted R-squared: 0.991
## F-statistic: 555 on 3 and 12 DF, p-value: 3.92e-13
vif(fit4)
## Unemployed Armed.Forces Year
## 3.32 2.22 3.89
#(f) (refer HW8i)
anova(fit,fit4)
## Analysis of Variance Table
##
## Model 1: Employed ~ GNP.deflator + GNP + Unemployed + Armed.Forces + Year +
## Population
## Model 2: Employed ~ Unemployed + Armed.Forces + Year
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 9 0.836
## 2 12 1.323 -3 -0.487 1.75 0.23