Concern over the weather associated with El Niño has increased interest in the possibility that the climate on earth is getting warmer. The most common theory relates an increase in atmospheric levels of carbon dioxide (CO2), a greenhouse gas, to increases in temperature. Here is a scatterplot showing the mean annual CO2 concentration in the atmosphere, measured in parts per million (ppm) at the top of Mauna Loa in Hawaii, and the mean annual air temperature over both land and sea across the globe, in degrees Celsius (C).
A regression predicting Temperature from CO2 produces the following output table (in part):
a) What is the correlation between CO2 and Temperature?
b) Explain the meaning of R-squared in this context.
c) Give the regression equation.
d) What is the meaning of the slope in this equation?
e) What is the meaning of the y-intercept of this equation?
f) Here is a scatterplot of the residuals vs. CO2. Does this plot show evidence of the violation of any assumptions behind the regression? If so, which ones?
g) CO2 levels will probably reach 364 ppm this year. What mean Temperature does the regression predict from that information?