Problem Set 5
MSDA3055 Linear Regression and Time Series
Due Date: March 29, 2021
Problem 1
(a) Obtain time series of real GDP and real consumption for a country of your choice. Provide details.
(b) Display time-series plots and a scatterplot (put consumption on the vertical axis).
(c) Convert your series to growth rates in percent, and again display time series plots.
(d) For each series, ,provide summary statistics (e.g., mean, standard deviation, range, skewness, kurtosis, …).
(e) Run a simple OLS linear regression in R and interpret its coefficient estimates.
(f) Interpret goodness-of-fit metrics for OLS linear regression.
(g) Relate R2 with correlation coefficient.
Problem 2
Monte Carlo experiment: Consider the following model:
Yi = ?1 + ?2Xi + ui
You are told that ?1 = 25,?2 = 0.5,? 2 = 9, and ui ? N(0, 9).
Assume ui ? N(0, 9), that is, ui are normally distributed with mean 0 and variance 9. Generate 10 sets of
64 observations on ui from the given normal distribution and use the 64 observations on X given in Table 2, to generate 100 sets of the estimated ? coefficients (each set will have the two estimated parameters). Take the averages of each of the estimated ? coefficients and relate them to the true values of these coefficients given above. What overall conclusion do you draw?