case1502 {Sleuth3}

Global Warming

Description

The data are the temperatures (in degrees Celsius) averaged for the northern hemisphere over a full year, for years 1850 to 2010. The 161-year average temperature has been subtracted, so each observation is the temperature difference from the series average.

Usage

case1502

Format

A data frame with 161 observations on the following 2 variables.

Year

year in which yearly average temperature was computed, from 1850 to 2010

Temperature

northern hemisphere temperature minus the 161-year average (degrees Celsius)

Source

Ramsey, F.L. and Schafer, D.W. (2013). The Statistical Sleuth: A Course in Methods of Data Analysis (3rd ed), Cengage Learning.

References

Jones, P.D., D. E. Parker, T. J. Osborn, and K. R. Briffa, (2011) Global and Hemispheric Temperature Anomalies and and Marine Instrumental Records, CDIAC, http://cdiac.ornl.gov/trends/temp/jonescru/jones.html, August 4, 2011.

See Also

ex1519

Examples

str(case1502)
attach(case1502)

## EXPLORATION AND MODEL BUILDING
plot(Temperature ~ Year, type="b")  # Type = "b" for *both* points and lines

yearSquared <- Year^2
yearCubed <- Year^3
myLm1 <- lm(Temperature ~ Year + yearSquared + yearCubed)
res1 <- myLm1$res
myPacf <- pacf(res1)  # Partial autocorrelation from residuals
r1 <- myPacf$acf[1]  #First serial correlation coefficient    
n <- length(Temperature)   # Series length = 161
v <- Temperature[2:n]  -  r1*Temperature[1:(n-1)]   # Filtered response
ones <- rep(1-r1, n-1)   # make a variable of all 1's
u1 <- Year[2:n]          -  r1*Year[1:(n-1)]   # Filtered "ones"
u2 <- yearSquared[2:n]  -  r1*yearSquared[1:(n-1)]  # Filtered X1
u3 <- yearCubed[2:n]    -  r1*yearCubed[1:(n-1)]  # Filtered X2
myLm2 <- lm(v ~  u1 + u2 + u3 )
res2 <- myLm2$res                                       
pacf(res2)   # Looks fine; don't worry about lag 4 marginal significance
plot(myLm2, which=1)  # Residual plot
summary(myLm2) # Cubic term isn't needed.
myLm3    <- update(myLm2, ~ . - u3) # Drop cubic term

## INFERENCE
summary(myLm3) # Everything remaining is statistically significant.

## GRAPHICAL DISPLAY FOR PRESENTATION
plot(Temperature ~ Year, xlab="Year",
  ylab=expression(paste("Annual Average Temperature (Difference From Average), ",
  degree,"C")),main="Annual Average Temperature in Northern Hemisphere; 1850-2010",
  type="b", pch=21, lwd=2, bg="green", cex=1.5)    
myFits <- myLm3$fit
lines(myFits ~ Year[2:161], col="blue", lwd=2)  
legend(1850,0.6,"Quadratic Regression Fit, Adjusted for AR(1) Serial Correlation",
  col="blue", lwd=2, box.lty=0)

detach(case1502)