Chapter 7: Hypothesis Tests and Confidence Intervals in Multiple Regression
Multiple Choice for the Web
1)
When testing joint hypothesis, you should
a. use t-statistics for each hypothesis and reject the null hypothesis is all of the
restrictions fail
b. use the F-statistic and reject all the hypothesis if the statistic exceeds the critical value
c. use t-statistics for each hypothesis and reject the null hypothesis once the statistic
exceeds the critical value for a single hypothesis
d. use the F-statistics and reject at least one of the hypothesis if the statistic exceeds the
critical value
2)
In the multiple regression model, the t-statistic for testing that the slope is significantly
different from zero is calculated
a.
b.
c.
d.
3)
by dividing the estimate by its standard error.
from the square root of the F-statistic.
by multiplying the p-value by 1.96.
using the adjusted R2 and the confidence interval.
If you wanted to test, using a 5% significance level, whether or not a specific slope
coefficient is equal to one, then you should
a. subtract 1 from the estimated coefficient, divide the difference by the standard error,
and check if the resulting ratio is larger than 1.96.
b. add and subtract 1.96 from the slope and check if that interval includes 1.
c. see if the slope coefficient is between 0.95 and 1.05.
d. check if the adjusted R2 is close to 1.
4)
When there are two coefficients, the resulting confidence sets are
a.
b
c
d
rectangles
ellipses
squares
trapezoids
1
5)
All of the following are true, with the exception of one condition:
2
a. a high R 2 or R does not mean that the regressors are a true cause of the dependent
variable
2
b. a high R 2 or R does not mean that there is no omitted variable bias
2
c. a high R 2 or R always means that an added variable is statistically significant
2
d. a high R 2 or R does not necessarily mean that you have the most appropriate set of
regressors
6)
You have estimated the relationship between test scores and the student-teacher ratio
under the assumption of homoskedasticity of the error terms. The regression output is as
  698.9  2.28  STR , and the standard error on the slope is 0.48. The
follows: TestScore
homoskedasticity-only “overall” regression F- statistic for the hypothesis that the
Regression R2 is zero is approximately
a.
b.
c.
d.
7)
Consider a regression with two variables, in which X1i is the variable of interest and X2i is
the control variable. Conditional mean independence requires
a.
b.
c.
d.
8)
0.96
1.96
22.56
4.75
E (ui | X 1i , X 2i )  E (ui | X 2i )
E (ui | X 1i , X 2i )  E (ui | X1i )
E (ui | X 1i )  E (ui | X 2i )
E (ui )  E (ui | X 2i )
The homoskedasticity-only F-statistic and the heteroskedasticity-robust F-statistic
typically are
a.
b.
c.
d.
the same
different
related by a linear function
a multiple of each other (the heteroskedasticity-robust F-statistic is 1.96 times the
homoskedasticity-only F-statistic)
2
9)
Consider the following regression output where the dependent variable is testscores and
the two explanatory variables are the student-teacher ratio and the percent of English
  698.9  1.10  STR  0.650  PctEL . You are told that the t-statistic
learners: TestScore
on the student-teacher ratio coefficient is 2.56. The standard error therefore is
approximately
a.
b.
c.
d.
10)
0.25
1.96
0.650
0.43
The critical value of F4, at the 5% significance level is
a.
b.
c.
d.
3.84
2.37
1.94
Cannot be calculated because in practice you will not have infinite number of
observations
3