case1502: Global Warming

In Sleuth2: Data Sets from Ramsey and Schafer's "Statistical Sleuth (2nd Ed)"

Description

The data are the temperatures (in degrees Celsius) averaged for the northern hemisphere over a full year, for years 1880 to 1987. The 108-year average temperature has been subtracted, so each observation is the temperature difference from the series average.

Usage

case1502

Format

A data frame with 108 observations on the following 2 variables.

Year

year in which yearly average temperature was computed, from 1880 to 1987

Temp

northern hemisphere temperature minus the 108-year average (degrees Celsius)

Source

Ramsey, F.L. and Schafer, D.W. (2002). The Statistical Sleuth: A Course in Methods of Data Analysis (2nd ed), Duxbury.

References

Jones, P.D. (1988). Hemispheric Surface Air Temperature Variations—Recent Trends Plus an Update to 1987, Journal of Climatology 1: 654–660.

Examples

str(case1502)

# Residuals from regression fit, ignoring autocorrelation
resids <- lm(Temp ~ Year, case1502)$res
# PACF plot shows evidence of 1st order auto correlation
acf(resids,type="partial")
# 1st autocorrelation coef.
acorr1 <- acf(resids,type="correlation",plot=FALSE)$acf[2] 

# Fit regression with filtered response and explanatory variables:
n <- length(case1502$Temp)
y <- with(case1502, Temp [2:n] - acorr1* Temp [1:(n-1)])
x <- with(case1502, Year [2:n] - acorr1* Year [1:(n-1)])
fit <- lm(y ~ x)
summary(fit)  # Interpret coefficient of x as coefficient of Year

Example output

'data.frame':	108 obs. of  2 variables:
 $ Year: num  1880 1881 1882 1883 1884 ...
 $ Temp: num  -0.31 -0.27 -0.31 -0.39 -0.48 ...

Call:
lm(formula = y ~ x)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.229613 -0.074123  0.003482  0.068846  0.200045 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -4.9268069  0.6154922  -8.005 1.71e-12 ***
x            0.0046035  0.0005809   7.924 2.56e-12 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.1016 on 105 degrees of freedom
Multiple R-squared:  0.3742,	Adjusted R-squared:  0.3683 
F-statistic:  62.8 on 1 and 105 DF,  p-value: 2.563e-12

Sleuth2 documentation built on May 2, 2019, 7:01 a.m.