library(faraway)
data("airpass")
attach(airpass)
plot(pass~year,type="l")
passmodel <- lm(pass~year)
summary(passmodel)
##
## Call:
## lm(formula = pass ~ year)
##
## Residuals:
## Min 1Q Median 3Q Max
## -93.858 -30.727 -5.757 24.489 164.999
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1474.771 61.106 -24.14 <2e-16 ***
## year 31.886 1.108 28.78 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 46.06 on 142 degrees of freedom
## Multiple R-squared: 0.8536, Adjusted R-squared: 0.8526
## F-statistic: 828.2 on 1 and 142 DF, p-value: < 2.2e-16
library(faraway)
data(aatemp)
names(aatemp)
## [1] "year" "temp"
attach(aatemp)
## The following object is masked from airpass:
##
## year
plot(temp~year,type="l")
abline(0,0)
tempmod <- lm(temp~year)
summary(tempmod)
##
## Call:
## lm(formula = temp ~ year)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.9843 -0.9113 -0.0820 0.9946 3.5343
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 24.005510 7.310781 3.284 0.00136 **
## year 0.012237 0.003768 3.247 0.00153 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.466 on 113 degrees of freedom
## Multiple R-squared: 0.08536, Adjusted R-squared: 0.07727
## F-statistic: 10.55 on 1 and 113 DF, p-value: 0.001533
tempmod <- lm(temp~year+I(year^2))
summary(tempmod)
##
## Call:
## lm(formula = temp ~ year + I(year^2))
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.0412 -0.9538 -0.0624 0.9959 3.5820
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.127e+02 3.837e+02 -0.554 0.580
## year 2.567e-01 3.962e-01 0.648 0.518
## I(year^2) -6.307e-05 1.022e-04 -0.617 0.539
##
## Residual standard error: 1.47 on 112 degrees of freedom
## Multiple R-squared: 0.08846, Adjusted R-squared: 0.07218
## F-statistic: 5.434 on 2 and 112 DF, p-value: 0.005591
library(faraway)
data(divusa)
attach(divusa)
## The following object is masked from aatemp:
##
## year
## The following object is masked from airpass:
##
## year
birthmod <- lm(birth~year+I(year^2))
summary(birthmod)
##
## Call:
## lm(formula = birth ~ year + I(year^2))
##
## Residuals:
## Min 1Q Median 3Q Max
## -24.2952 -11.8939 -0.7406 12.5154 26.3901
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.428e+04 1.464e+04 -3.709 0.000400 ***
## year 5.604e+01 1.495e+01 3.748 0.000351 ***
## I(year^2) -1.444e-02 3.818e-03 -3.782 0.000313 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 14.8 on 74 degrees of freedom
## Multiple R-squared: 0.4403, Adjusted R-squared: 0.4252
## F-statistic: 29.11 on 2 and 74 DF, p-value: 4.718e-10
residuals <- birthmod$residuals
plot(residuals,year)
library(lmtest)
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
dwtest(birthmod)
##
## Durbin-Watson test
##
## data: birthmod
## DW = 0.07405, p-value < 2.2e-16
## alternative hypothesis: true autocorrelation is greater than 0