solution

The data file co2data.csv contains monthly mean atmospheric CO₂ concentrations measured at Mauna Loa, Hawaii, from January 1959 to December 2003. Atmospheric CO₂ concentrations show a distinct seasonal pattern, reflecting the annual cycle of plant activities. The data set has four columns: CO₂ (monthly CO₂ concentrations in ppm), mon (calendar month), year, and months (months since January 1959). The data plot (Figure 6.30) showed an unmistakable increasing temporal trend in CO₂ concentrations. In this question you are asked to quantify the magnitude of this increase. A frequently used statistical method for estimating temporal trend is to fit a linear regression model of the CO₂ concentration against a time variable (e.g., number of months since a starting point). In this case, the column months in the data set is such a time variable.

(a) Fit a simple regression model using CO₂ as the response variable and months as the predictor variable. Quantify the temporal trend (monthly or annual rate of increase in CO₂ concentration) and discuss the potential problems of the model. (Hint: plot the residuals against months.)

(b) Refit the model by using mon as a second (factor) predictor and explain the temporal trend in CO₂ concentrations.

In both models, the residuals versus fitted plot shows a systematic pattern. What may be the cause of such pattern?