Description
1. There have been many studies documenting that the average global temperature has been
increasing over the last century. The consequences of a continued rise in global temperature will
be dire. Rising sea levels and an increased frequency of extreme weather events will affect
billions of people.
In this problem, we will attempt to study the relationship between average
global temperature and several other factors. The file ClimateChange.csv contains climate data
from May 1983 to December 2008. The available variables are described in Table 1.
Variable Description
Year The observation year.
Month The observation month.
Temp The difference in degrees Celsius between the average global temperature
in the observation month and a reference value
CFC.11 The atmospheric concentration of trichlorofluoromethane (CFC-11),
expressed in ppbv (parts per billion by volume).
CFC.12 The atmospheric concentration of dichlorodifluoromethane (CFC-12),
expressed in ppbv.
CO2 The atmospheric concentration of carbon dioxide (CO2), expressed in ppmv
(parts per million by volume).
N2O The atmospheric concentration of nitrous oxide (N2O), expressed in ppmv.
CH4 The atmospheric concentration of methane (CH4), expressed in ppmv.
Aerosols The mean stratospheric aerosol optical depth at 550 nm. This variable is
linked to volcanoes, as volcanic eruptions result in new particles being
added to the atmosphere, which affect how much of the sun’s energy is
reflected back into space.
TSI The total solar irradiance (TSI) in W/m2 (the rate at which the sun’s energy
is deposited per unit area). Due to sunspots and other solar phenomena,
the amount of energy that is given off by the sun varies substantially with
time.
MEI Multivariate El Nino Southern Oscillation index (MEI), a measure of the
strength of a weather effect in the Pacific Ocean that affects global
temperatures.
Table 1: Variables in the dataset ClimateChange.csv.
a) Start by splitting the dataset into a training set, consisting of observations up to and
including 2006, and a testing set, consisting of observations after 2006. You will use the
training set to build your model, and the testing set to evaluate the predictive ability of your
model. (You can split the dataset manually in excel, and store them as two csv files.
Alternatively, you can split the dataset in R and this will be demonstrated in lecture around
the end of March)
Then, build a linear regression model to predict Temp, using all of the other variables as
independent variables (except Year and Month). You should use the training set that you
just created to build the model.
(i) What is the linear regression equation produced by your model?
(ii) Evaluate the quality of the model. What is the R2 value? (Note that this is called
“Multiple R-squared” in R). Which independent variables are significant?
(iii) Current scientific opinion is that N2O and CFC-11 are greenhouse gasses: gasses that
are able to trap heat from the sun and contribute to the heating of the Earth.
However, you should see that the regression coefficient of both the N2O and CFC.11
variables in this model are negative, indicating that increasing atmospheric
concentrations of either of these two components is associated with lower global
temperatures. What is the simplest explanation for this contradiction?
(iv) Compute the correlations between all independent variables in the training set.
Which independent variables is N2O highly correlated with (absolute correlation
greater than 0.7)? Which independent variables is CFC.11 highly correlated with?
b) Now build a new linear regression model, this time only using MEI, TSI, Aerosols, and N2O as
the independent variables. Remember to use the training set to build the model.
(i) How does the coefficient for N2O in this model compare to the coefficient in the
previous model?
(ii) How does the quality of this model compare to the previous one? Consider the R2
value and the significance of the independent variables when answering this
question.
c) We have developed an understanding of how well we can fit a linear regression model to
the training data, but now we what see if the model quality holds when applied to unseen
data. Using the simplified model you created in part (b), calculate predictions for the testing
dataset. What is the R2 on the test set? What does this tell you about the model?
