Assignment 7 Economics 31 Fall 1999
Hypothesis Testing with Regression Coefficients
Reading: Mirer Chtr. 11,12,13 Beals Chtr. 9,10,11
Hypothesis Testing with Regression Coefficients
1. Write out the steps for doing a hypothesis test, for
calculating R2, and
define adjusted R2 Why are significance tests crucial to
regression
analysis? The rest of this assignment will require the use of the
statistical package STATA and the data file cps22an (see Ass2 for aid
in
using STATA).
2. a) Using the data in the file estimate the linear relationship
between
the hourly wage, and the years of experience as an independent
variable.
b) Draw a diagram of the sampling distribution of the coefficient
on
experience, explain the meaning of the standard deviation, and show
the mean.
c) Test the hypothesis that the coefficient, EX is = to 0. Write
out the
null and alternative hypothesis, the significance level, and show
all
intermediate steps.
d) Construct a confidence interval for EX, and explain the meaning
of this
interval.
3. a) Using the data in the file estimate the linear relationship
between
hourly wage, EX, and ED.
b) Draw a sampling distribution of the coefficients on experience,
explain
the meaning of the standard deviation, and show the mean.
c) Test the hypothesis that the coefficient on EX is insignificant
(ie
insignificantly different from 0). Write out the null and
alternative
hypothesis, the significance level, and show all intermediate
steps,
d) Construct a confidence interval for EX, and explain the meaning
of this
interval.
e) Compare the R2 values from 1 and 2. Explain the
meaning of R2
in the simple and multiple regression.
f) Test the hypothesis that ED has no independent effect on hourly
wage, ie
ED coefficient=0 at the 5% significance level.
4. a) Using the data in the file estimate the linear relationship
between
hourly wage, AGE, MARR, FE, and MARR*FE (see Ass2 for instructions
on
creating MARR*FE).
b) Explain your results (interpret the coefficients).
c) Test the individual significance of the constant and each of
the
coefficients.
5. a) Using the data in the file estimate the relationship between
hourly
wage, AGE, MARR, FE, MARR*FE, and SOUTH.
b) Explain your results (interpret the coefficients).
c) Test the individual significance of the constant and each of
the
coefficients.
d) Discuss the effect of the inclusion of SOUTH on the other
coefficients.
Did the significance of any coefficients change? Explain why this may
or
may not happen.