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chapter 5
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Questions in this quiz (24)
1Heteroskedasticity means that
- Ahomogeneity cannot be assumed automatically for the model.
- Bthe variance of the error term is not constant.
- Cthe observed units have different preferences.
- Dagents are not all rational.
2With heteroskedastic errors, the weighted least squares estimator is BLUE. You should use OLS with heteroskedasticity-robust standard errors because
- Athis method is simpler.
- Bthe exact form of the conditional variance is rarely known.
- Cthe Gauss-Markov theorem holds.
- Dyour spreadsheet program does not have a command for weighted least squares.
3When estimating a demand function for a good where quantity demanded is a linear function of the price, you should
- Anot include an intercept because the price of the good is never zero.
- Buse a one-sided alternative hypothesis to check the influence of price on quantity.
- Cuse a two-sided alternative hypothesis to check the influence of price on quantity.
- Dreject the idea that price determines demand unless the coefficient is at least 1.96.
4The t-statistic is calculated by dividing
- Athe OLS estimator by its standard error.
- Bthe slope by the standard deviation of the explanatory variable.
- Cthe estimator minus its hypothesized value by the standard error of the estimator.
- Dthe slope by 1.96.
5The confidence interval for the sample regression function slope
- Acan be used to conduct a test about a hypothesized population regression function slope.
- Bcan be used to compare the value of the slope relative to that of the intercept.
- Cadds and subtracts 1.96 from the slope.
- Dallows you to make statements about the economic importance of your estimate.
6If the absolute value of your calculated t-statistic exceeds the critical value from the standard normal distribution, you can
- Areject the null hypothesis.
- Bsafely assume that your regression results are significant.
- Creject the assumption that the error terms are homoskedastic.
- Dconclude that most of the actual values are very close to the regression line.
7Under the least squares assumptions (zero conditional mean for the error term, Xi and Yi being i.i.d., and Xi and ui having finite fourth moments), the OLS estimator for the slope and intercept
- Ahas an exact normal distribution for n > 15.
- Bis BLUE.
- Chas a normal distribution even in small samples.
- Dis unbiased.
8 Consider the following regression line: test scores = 698.9 – 2.28 × STR. You are told that the t-statistic on the slope coefficient is 4.38. What is the standard error of the slope coefficient?
- A0.52
- B1.96
- C-1.96
- D4.38
9Imagine that you were told that the t-statistic for the slope coefficient of the regression line test score = 698.9 – 2.28 × STR was 4.38. What are the units of measurement for the t-statistic?
- Apoints of the test score
- Bnumber of students per teacher
- Ctest score/ STR
- Dstandard deviations
10The construction of the t-statistic for a one- and a two-sided hypothesis
- Adepends on the critical value from the appropriate distribution.
- Bis the same.
- Cis different since the critical value must be 1.645 for the one-sided hypothesis, but 1.96 for the two-sided hypothesis (using a 5% probability for the Type I error).
- Duses ±1.96 for the two-sided test, but only +1.96 for the one-sided test.
11The p-value for a one-sided left-tail test is given by
- APr(Z - tact ) = φ(tact).
- BPr(Z < tact ) = φ(tact).
- CPr(Z < tact ) < 1.645.
- Dcannot be calculated, since probabilities must always be positive.
12One of the following steps is not required as a step to test for the null hypothesis:
- Acompute the standard error of B hat 1.
- Btest for the errors to be normally distributed.
- Ccompute the t-statistic.
- Dcompute the p-value.
13Finding a small value of the p-value (e.g. less than 5%)
- Aindicates evidence in favor of the null hypothesis.
- Bimplies that the t-statistic is less than 1.96.
- Cindicates evidence against the null hypothesis.
- Dwill only happen roughly one in twenty samples.
14The only difference between a one- and two-sided hypothesis test is
- Athe null hypothesis.
- Bdependent on the sample size n.
- Cthe sign of the slope coefficient.
- Dhow you interpret the t-statistic.
15A binary variable is often called a
- Adummy variable.
- Bdependent variable.
- Cresidual.
- Dpower of a test.
16In the presence of heteroskedasticity, and assuming that the usual least squares assumptions hold, the OLS estimator is
- Aefficient.
- BBLUE.
- Cunbiased and consistent.
- Dunbiased but not consistent.
17The proof that OLS is BLUE requires all of the following assumptions with the exception of:
- Athe errors are homoskedastic.
- Bthe errors are normally distributed.
- CE(ui I Xi) =0
- Dlarge outliers are unlikely.
18If the errors are heteroskedastic, then
- AOLS is BLUE.
- BWLS is BLUE if the conditional variance of the errors is known up to a constant factor of proportionality.
- CLAD is BLUE if the conditional variance of the errors is known up to a constant factor of proportionality.
- DOLS is efficient.
19The homoskedastic normal regression assumptions are all of the following with the exception of:
- Athe errors are homoskedastic.
- Bthe errors are normally distributed.
- Cthere are no outliers.
- Dthere are at least 10 observations.
20Using the textbook example of 420 California school districts and the regression of testscores on the student-teacher ratio, you find that the standard error on the slope coefficient is 0.51 when using the heteroskedasticity robust formula, while it is 0.48 when employing the homoskedasticity only formula. When calculating the t-statistic, the recommended procedure is to
- Ause the homoskedasticity only formula because the t-statistic becomes larger
- Bfirst test for homoskedasticity of the errors and then make a decision
- Cuse the heteroskedasticity robust formula
- Dmake a decision depending on how much different the estimate of the slope is under the two procedures
21Consider the estimated equation from your textbook
=698.9 - 2.28 STR, R2 = 0.051, SER = 18.6
(10.4) (0.52)
The t-statistic for the slope is approximately- A4.38
- B67.20
- C0.52
- D1.76
22You have collected data for the 50 U.S. states and estimated the following relationship between the change in the unemployment rate from the previous year (change in ur hat ) and the growth rate of the respective state real GDP (gy). The results are as follows
(change in ur hat) = 2.81 — 0.23 gy, R2= 0.36, SER = 0.78
(0.12) (0.04)
Assuming that the estimator has a normal distribution, the 95% confidence interval for the slope is approximately the interval- A[2.57, 3.05]
- B[-0.31,0.15]
- C[-0.31, -0.15]
- D[-0.33, -0.13]
23Using 143 observations, assume that you had estimated a simple regression function and that your estimate for the slope was 0.04, with a standard error of 0.01. You want to test whether or not the estimate is statistically significant. Which of the following possible decisions is the only correct one:
- Ayou decide that the coefficient is small and hence most likely is zero in the population
- Bthe slope is statistically significant since it is four standard errors away from zero
- Cthe response of Y given a change in X must be economically important since it is statistically significant
- Dsince the slope is very small, so must be the regression R2.
24You extract approximately 5,000 observations from the Current Population Survey (CPS) and estimate the following regression function:
ahe hat = 3.32 — 0.45 Age, R2= 0.02, SER = 8.66
(1.00) (0.04)
where ahe is average hourly earnings, and Age is the individual's age. Given the specification, your 95% confidence interval for the effect of changing age by 5 years is approximately- A[$1.96, $2.54]
- B[$2.32, $4.32]
- C[$1.35, $5.30]
- Dcannot be determined given the information provided
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- Regression with a Single Regressor: Hypothesis Tests and Confidence Intervals
- Author
- kiran syed
- Language
- English
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