EC 420, Spring 2008
Show all necessary work.
You will have the entire class period to complete this exam.
This exam is “open book” but “closed note”; you may use the course text (Wooldridge),
but notes, old homework questions and answers, etc., are strictly forbidden.
Part One (short answer and proof)
1. What is a sampling distribution?
What does the Central Limit Theorem state, and
why is it so awesome (important for us statisticians)? (3 points)
A sampling distribution describes how a sample statistic (such as the sample mean,
the sample regression slope, the sample regression intercept, etc) varies from one
sample to the next.
The Central Limit Theorem is indeed awesome – it says that the
sampling distribution of the sample mean and sample regression “betas” are all
approximately normally distributed, as long as the sample size is “large enough”
(n>20 is a typical rule of thumb).
It is important because it means that we can
compute the probability of observing a particular sample statistics if we knew the
population parameter – this is fundamental for computing p-values and doing
2. What are the similarities between the slope of a simple regression line, the correlation
between two variables, and the r-squared of a simple regression model?
What are the
differences? (3 points)
If the r-squared equals zero, so does the correlation and the slope coefficient.
correlation and the slope coefficient always are the same sign, and the r-squared just
equals the square of the correlation between
The differences are that, while the slope tells us how steep a regression line is, it does
not really tell us how well the line fits the data…the correlation and the r-squared do
3. Consider the following data for (
): (1,2), (4,5), (1,4), (3,5) and (4,7). I run a
, and I find that
= 1 and
= 2. (3 points)
a. Graph the underlying data.
b. Graph the predicted values for each observation.
c. Graph the regression line.
d. Indicate the residuals for each observation.