AirPassengers in R

This is monthly airline passenger number frm 1949-1961. There is 144 obervation in the dataset, and no missing data. The unit is in thousands.

data(AirPassengers)
str(AirPassengers)
##  Time-Series [1:144] from 1949 to 1961: 112 118 132 129 121 135 148 148 136 119 ...
summary(AirPassengers)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   104.0   180.0   265.5   280.3   360.5   622.0
plot(AirPassengers, ylab="Passengers (1000s)", type="o", pch =20, col="red")

Use decompose function to oberver time-series data using moving averages.

AirPassengers.decompM <- decompose(AirPassengers, type = "multiplicative")
plot(AirPassengers.decompM)

t <- seq(1, 144, 1)
lm_number<-lm(AirPassengers.decompM$trend~ t )
summary(lm_number)
## 
## Call:
## lm(formula = AirPassengers.decompM$trend ~ t)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -22.9162  -6.0845   0.6094   5.8658  23.4748 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 84.64827    2.05100   41.27   <2e-16 ***
## t            2.66694    0.02504  106.50   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 10.96 on 130 degrees of freedom
##   (12 observations deleted due to missingness)
## Multiple R-squared:  0.9887, Adjusted R-squared:  0.9886 
## F-statistic: 1.134e+04 on 1 and 130 DF,  p-value: < 2.2e-16
plot(lm_number)