UNIVERSITY OF CALIFORNIA, LOS ANGELES
Department of Economics
Economics 143 (Cameron) - Applied Regression
Analysis
Computing Lab Session #3:
Distribution of Sample Regression Functions
Tasks to be Performed
- Using TED, copy the program n:plotsrf.sha
from the network (or download
it from the Web site) to your c: or a: drive, so that it can be
edited.
- While you are in TED, note the location specified for the READ file and alter
this as
necessary to reflect the location from which you will be reading the data file,
which is called n:table5_1.dat on the network.
You will probably be
writing your output to the screen, so file 6 need not be
specified.
- Preliminaries: Look over the contents of the program so
you have a feel for what tasks will
be performed.
- Find the OLS regression that uses the entire population of 55 observations.
- Find the block of commands enclosed by do #=1,[nsim] at the beginning
and endo at the end. Each time the program loops through this set of
commands, the character # is replaced in the code by the number of the current
iteration.
- Notice the use of the sort and sample commands to obtain
different random samples from the population of 55 observations.
- Note the options on the ols commands (within this "do-loop") that
save
the fitted coefficients from each regression (coef=)as well as the vector
of fitted values for the dependent variable (predict=).
- If you enjoy the challenge, review the basic matrix commands in SHAZAM and
figure out what is happening in the matrix and copy commands. Don't
panic if you do not know matrix algebra. This program is also just a tool to
demonstrate an important point. You will not be expected to write SHAZAM code of
this complexity during the course.
- Find the crucial plot commands. When the sample is set to
sample 1 [nsamsim], the plot qdd pdd / gnu will display the range of
alternative fitted sample regression functions from alternative samples. When the
sample is set to sample 1 [nsim], the plot bb1 bb2 / gnu will show
the
correlation between the slope and the intercept estimates across the different
sample regressions we will be estimating.
- Before exiting TED, change the value of the number of simulations by altering
the nsim:100 statement to nsim:20. The nsamsim:1000
statement will have to be changed accordingly to nsamsim:200. This will
help if the simultaneous execution of a large number of SHAZAM programs on the
network slows the system to a crawl (as it used to do in the old lab). Use F7 to
save the program on your c:\ or a: drive and exit.
- Now, run the plotsrf.sha program. Have a pencil and paper handy. When
the program first pauses, you should be able to see the regression estimates for
the entire population (all 55 observations). Note these "true" values for the
slope and intercept parameters.
- Hit the enter key and watch the program go through the iterations. In each
iteration, a separate random sample is drawn, and a sample regression function is
calculated. When you get to the next pause, make a note of the recommended form
of the first plot command, given the values you have established for the number of
simulations. Hit enter to continue.
- At the next pause, note the second set of plotting instructions for the
current run of the program. Hit enter to continue.
- When you get to the TYPE COMMAND prompt, issue the recommended plotting
commands and observe what happens.
- Questions:
- When we study "confidence intervals for prediction," in simple regression,
we will derive the shape of the distribution of sample regression fitted values
around the true population regression function. Describe what shape you expect
this confidence band to have, based on the evidence in your simulations. (You may
need to try 50 or 100 simulations to get a clear sense of this
shape.)
- How would you describe the shape of the sampling distribution of intercepts?
Of slopes? (Again, you may need 100 simulations to see a tendency.)
- What is the relationship between the slope and the intercept across your
different random samples from the population and the different sample regression
functions they produce? Are they correlated? How? Is this logical?
Updated: February 2, 1998
Prepared by: Trudy Ann Cameron