See questions below on "disturbances""
-in the regression model:
y = Xb + e
where yhat = Xb
The disturbances, or errors, represent the difference between Xb (yhat)
and y. In the real world, we do not know the true errors or disturbances.
We simply have estimates of them, in the form of the regression residuals.
(This is because we have a sample of y values from some distribution
rather than a set of fixed y's.)
One of our OLS regression assumptions is that the disturbances follow a
normal distribution that is centered at zero. This means that the
E[error] = 0. To evaluate whether or not this assumption holds, we look
at our residuals. These are not exactly the same as the true
disturbances, but the best material we have to work with. This is why we
are comparing the distribution of the residuals with a t distribution
rather than a normal--to reflect this added uncertainty.
I looked at the distribution of the y values in the handout example after
looking at the distribution of the residuals in the qq.plot because I
wanted to see if a skew in the distribution of the y values might be
partially responsible for the skew in the residual distribution. You can
see how the two are linked directly from the equation above.
On White's estimator, see p. 305 in Fox. It is calculate different,
robust standard errors for the coefficients using the residuals from the
regression. White's method does not calculate new regression
coefficients.
The last homework assignment will be due the last day of lecture.
Good luck!
Alison
Hi Alison,
I have a couple questions on for the material this week:
1. What, exactl, does "non-normality of disturbances" mean? It seems
that we are checking to make sure that the y variable follows the
t-distribution by looking at qq plots and histograms. Is this right? Or
what is meant by a "disturbance"? I am getting a litle tripped up on the
vocab.
2. What does the White heteroscedasticity consistent covariance estimator
do exactly? In the homework I used it to recalculate the standard errors
of the regression coefficient estimates. Does using the White method not
alter the actual regression coefficient estimates? I see that the White
method is
used to correct the estimate of the variance of our regression
coefficient estimates - is the variance in our regression coefficient
estimates measured by the standard errors?
Oh, one more question: what is the due date of our
last homework?