Econometric test

A binary variable is often called a a. dummy variable b. dependent variable c. residual d. power of a test

A

Consider the estimated equation from your textbook TestScore = 698.9 - 2.28*STR, R2 = 0.051, SER = 18.6 (10.4) (0.52) The t-statistic for the slope is approximately a. 4.38 b. 67.20 c. 0.52 d. 1.76

A

Consider the following regression line: =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? A) 0.52 B) 1.96 C) -1.96 D) 4.38

A

If the absolute value of your calculated t-statistic exceeds the critical value from the standard normal distribution, you can a. reject the null hypothesis. b. safely assume that your regression results are significant. c. reject the assumption that the error terms are homoskedastic. d. conclude that most of the actual values are very close to the regression line.

A

In which of the following relationships does the intercept have a real-world interpretation? a. the relationship between the change in the unemployment rate and the growth rate of real GDP ("Okun's Law") b. the demand for coffee and its price c. test scores and class-size d. weight and height of individuals

A

The OLS estimator is derived by A) minimizing the sum of squared residuals. B) minimizing the sum of absolute residuals. C) making sure that the standard error of the regression equals the standard error of the slope estimator. D) connecting the Yi corresponding to the lowest Xi observation with the Yi corresponding to the highest Xi observation.

A

The main advantage of using multiple regression analysis over differences in means testing is that the regression technique A) gives you quantitative estimates of a unit change in X. B) assumes that the error terms are generated from a normal distribution. C) allows you to calculate p-values for the significance of your results. D) provides you with a measure of your goodness of fit.

A

The slope estimator, B1, has a smaller standard error, other things equal, if a. there is more variation in the explanatory variable, X. b. there is a large variance of the error term, u. c. the sample size is smaller. d. the intercept, B0, is small.

A

To decide whether or not the slope coefficient is large or small, a. you should analyze the economic importance of a given increase in X. b. the slope coefficient must be larger than one. c. the slope coefficient must be statistically significant. d. you should change the scale of the X variable if the coefficient appears to be too small.

A

Which of the following statements is correct? a. TSS = ESS + SSR b. ESS = SSR + TSS c. ESS > TSS d. R2 = 1 - (ESS/TSS)

A

With heteroskedastic errors, the weighted least squares estimator is BLUE. You should use OLS with heteroskedasticity-robust standard errors because A) the exact form of the conditional variance is rarely known. B) the Gauss-Markov theorem holds. C) this method is simpler. D) our spreadsheet program does not have a command for weighted least squares

A

You extract approximately 5,000 observations from the Current Population Survey (CPS) and estimate the following regression function:=3.32 —0.45Age, R2=0.02, SER=8.66(1.00) (0.04)where aheis average hourly earnings, and Ageis 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] D) cannot be determined given the information provided

A

If the errors are heteroskedastic, then a. OLS is BLUE b. WLS is BLUE if the conditional variance of the errors is known up to a constant factor of proportionality c. LAD is BLUE if the conditional variance of the errors is known up to a constant factor of proportionality d. OLS is efficient

B

In the simple linear regression model Y= B0+B1Xi+ui, a. the intercept is typically small and unimportant. b. B0+B1Xi represents the population regression function. c. the absolute value of the slope is typically between 0 and 1. d. B0+B1Xi represents the sample regression function.

B

Multiplying the dependent variable by 100 and the explanatory variable by 100,000 leaves the A) heteroskedasticity-robust standard errors of the OLS estimators the same. B) regression R2 the same. C) OLS estimate of the intercept the same. D) OLS estimate of the slope the same.

B

The OLS residuals, ^ui (mu hat) , are sample counterparts of the population a. regression function slope b. errors c. regression function's predicted values d. regression function intercept

B

The p-value for a one-sided left-tail test is given by A) Pr(Z-tact) =φ(tact). B) Pr(Z<tact) =φ(tact). C) Pr(Z<tact) <1.645. D) cannot be calculated, since probabilities must always be positive

B

The regression R2 is a measure of a. whether or not X causes Y. b. the goodness of fit of your regression line. c. whether or not ESS > TSS. d. the square of the determinant of R.

B

The regression R2 is a measure of a. whether or not X causes Y. b. the goodness of fit of your regression line. c. whether or not ESS > TSS. d. the square of the determinant of R.

B

The sample average of the OLS residuals is a. some positive number since OLS uses squares. b. zero. c. unobservable since the population regression function is unknown. d. dependent on whether the explanatory variable is mostly positive or negative.

B

Using 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 decisions is the only correct one: a. you decide that the coefficient is small and hence most likely is zero in the population b. the slope is statistically significant since it is four standard errors away from zero c. the response of Y given a change in X must be economically important since it is statistically significant d. since the slope is very small, so must be the regression R2 .

B

When estimating a demand function for a good where quantity demanded is a linear function of the price, you should a. not include an intercept because the price of the good is never zero. b. use a one-sided alternative hypothesis to check the influence of price on quantity. c. use a two-sided alternative hypothesis to check the influence of price on quantity. d. reject the idea that price determines demand unless the coefficient is at least 1.96.

B

he following are all least squares assumptions with the exception of: A) The conditional distribution of uigiven Xihas a mean of zero. B) The explanatory variable in regressionmodel is normally distributed .C) (Xi, Yi), i=1,..., nare independently and identically distributed. D) Large outliers are unlikely.

B

Changing the units of measurement, e.g. measuring test scores in 100s, will do all of the following EXCEPT for changing the a. residuals b. numerical value of the slope estimate c. interpretation of the effect that a change in X has on the change in Y d. numerical value of the intercept

C

Finding a small value of the p-value (e.g. less than 5%) A) indicates evidence in favor of the null hypothesis. B) implies that the t-statistic is less than 1.96. C) indicates evidence in against the null hypothesis. D) will only happen roughly one in twenty samples.

C

If you had a two regressor regression model, then omitting one variable which is relevant A) makes the sum of the product between the included variable and the residuals different from 0. B) will have no effect on the coefficient of the included variable if the correlation between the excluded and the included variable is negative. C) can result in a negative value for the coefficient of the included variable, even though the coefficient will have a significant positive effect on Y if the omitted variable were included. D) will always bias the coefficient of the included variable upwards.

C

In the linear regression model Yi= B0+ B1Xi+ ui, B0+ B1Xi is referred to as a. exogenous variation b. the sample regression function c. the population regression function d. the right- hand variable or regressor

C

In the simple linear regression model, the regression slope a. indicates by how many percent Y increases, given a one percent increase in X. b. when multiplied with the explanatory variable will give you the predicted Y. c. indicates by how many units Y increases, given a one unit increase in X. d. represents the elasticity of Y on X.

C

Interpreting the intercept in a sample regression function is a. not reasonable because you never observe values of the explanatory variables around the origin. b. reasonable because under certain conditions the estimator is BLUE. c. reasonable if your sample contains values of Xi around the origin. d. not reasonable because economists are interested in the effect of a change in X on the change in Y.

C

Interpreting the intercept in a sample regression function is A) not reasonable because you never observe values of the explanatory variables around the origin. B) reasonable because under certain conditions the estimator is BLUE. C) reasonable if your sample contains values of Xi around the origin. D) not reasonable because economists are interested in the effect of a change in Xon the change in Y

C

The sample regression line estimated by OLS A) has an intercept that is equal to zero. B) cannot have negative and positive slopes. C) is the line that minimizes the sum of squared prediction mistakes. D) is the same as the population regression line.

C

The t-statistic is calculated by dividing A) the OLS estimator by its standard error. B) the slope by 1.96. C) the estimator minus its hypothesized value by the standard error of the estimator. D) the slope by the standard deviation of the explanatory variable.

C

The t-statistic is calculated by dividing a. the OLS estimator by its standard error. b. the slope by the standard deviation of the explanatory variable. c. the estimator minus its hypothesized value by the standard error of the estimator. d. the slope by 1.96.

C

The variance of Yi is given by A. B20+ B21var(Xi) + var (ui) B. The variance of ui C. B21var(Xi) + var (ui) D. The variance of the residuals

C

To decide whether the slope coefficient indicates a "large" effect of X on Y, you look at the a. size of the slope coefficient b. regression 2 R c. economic importance implied by the slope coefficient d. value of the intercept

C

To obtain the slope estimator using the least squares principle, you divide the a. sample variance of X by the sample variance of Y. b. sample covariance of X and Y by the sample variance of Y. c. sample covariance of X and Y by the sample variance of X. d. sample variance of X by the sample covariance of X and Y.

C

Under imperfect multicollinearity A) the OLS estimator is biased even in samples of n > 100. B) the OLS estimator cannot be computed. C) two or more of the regressors are highly correlated. D) the error terms are highly, but not perfectly, correlated.

C

Using the textbook example of 420 California school districts and the regression of test scores 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 a. use the homoskedasticity only formula because the t-statistic becomes larger b. first test for homoskedasticity of the errors and then make a decision c. use the heteroskedasticity robust formula d. make a decision depending on how much different the estimate of the slope is under the two procedures

C

When the estimated slope coefficient in the simple regression model,^B1 , is zero, then a. R2 = -Y(Y bar). b. 0 < R2 < 1. c. R2 = 0. d. R2 > (SSR/TSS).

C

You 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) and the growth rate of the respective state real GDP (gy). The results are as follows chang in ur = 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]

C

the 95% confidence interval for B1 is the interval a. (B1- 1.96 SE (B1 ), B1+ 1.96 SER( B1)) b. (^B1- 1.645 SE (^B1 ), ^B1+ 1.645 SER( ^B1)) c. (^B1- 1.96SE (^B1 ), ^B1+ 1.96 SER( ^B1)) d. (^B1- 1.96, ^B1+ 1.96)

C

) Under 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 A) is BLUE. B) has an exact normal distribution for n > 15. C) has a normal distribution even in small samples. D) is unbiased.

D

Assume that you have collected a sample of observations from over 100 households and their consumption and income patterns. Using these observations, you estimate the following regression Ci= B0+B1Yi+ui,, where C is consumption and Y is disposable income. The estimate of B1 will tell you a.Chang in Income/ Chang in Consumption b. The amount you need to consume to survive c. Chang in Consumption/ Chang in Income d. Chang in Consumption/ Chang in Income

D

Binary variables a. are generally used to control for outliers in your sample. b. can take on more than two values. c. exclude certain individuals from your sample. d. can take on only two values.

D

E(ui | Xi) = 0 says that A) the sample mean of the Xs is much larger than the sample mean of the errors. B) dividing the error by the explanatory variable results in a zero (on average). C) the sample regression function residuals are unrelated to the explanatory variable. D) the conditional distribution of the error given the explanatory variable has a zero mean

D

E(ui | Xi) = 0 says that a. dividing the error by the explanatory variable results in a zero (on average). b. the sample regression function residuals are unrelated to the explanatory variable. c. the sample mean of the Xs is much larger than the sample mean of the errors. d. the conditional distribution of the error given the explanatory variable has a zero mean.

D

If you reject a joint null hypothesis using the F-test in a multiple hypothesis setting, then A) the regression is always significant. B) the F-statistic must be negative. C) all of the hypotheses are always simultaneously rejected. D) a series of t-tests may or may not give you the same conclusion.

D

Imagine that you were told that the t-statistic for the slope coefficient of the regression line TestScore=698.9- 2.28* STR was 4.38. What are the units of measurement for the t-statistic? a. points of the test score. b. number of students per teacher. c. TestScore/ STR d. standard deviations

D

The confidence interval for the sample regression function slope A) allows you to make statements about the economic importance of your estimate. B) can be used to compare the value of the slope relative to that of the intercept. C) adds and subtracts 1.96 from the slope. D) can be used to conduct a test about a hypothesized population regression function slope.

D

The reason why estimators have a sampling distribution is that a. economics is not a precise science. b. individuals respond differently to incentives. c. in real life you typically get to sample many times. d. the values of the explanatory variable and the error term differ across samples.

D

The sample regression line estimated by OLS a. will always have a slope smaller than the intercept. b. is exactly the same as the population regression line. c. cannot have a slope of zero. d. will always run through the point ( -X,-Y).(X bar and Y bar)

D

To decide whether or not the slope coefficient is large or small, A) the slope coefficient must be statistically significant. B) the slope coefficient must be larger than one. C) you should change the scale of the X variable if the coefficient appears to be too small. D) you should analyze the economic importance of a given increase in X.

D

You extract approximately 5,000 observations from the Current Population Survey (CPS) and estimate the following regression function: AHE = 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] d. cannot be determined given the information provided

D

he only difference between a one-and two-sided hypothesis test is A) the null hypothesis. B) dependent on the sample size n. C) the sign of the slope coefficient. D) how you interpret the t-statistic.

D

Heteroskedasticity means that a. homogeneity cannot be assumed automatically for the model. b. the variance of the error term is not constant. c. the observed units have different preferences. d. agents are not all rational.

b

With heteroskedastic errors, the weighted least squares estimator is BLUE. You should use OLS with heteroskedasticity-robust standard errors because a. this method is simpler. b. the exact form of the conditional variance is rarely known. c. the Gauss-Markov theorem holds. e. your spreadsheet program does not have a command for weighted least squares.

b