Statistics HW 2

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Question 1

Suppose you estimate the following the degree to which HDTV sales (in millions of units) are related to price, consumer income, and a time-trend as (p-values in parentheses)

You should conclude that the data do

		not exhibit a time-trend because the estimated coefficient for Price is not statistically significant.
		exhibit a time-trend because the estimated coefficient for Income is positive and statistically significant.
		not exhibit a time-trend because the estimated coefficient for the Time Trend is positive.
		exhibit a time-trend because the estimated coefficient for the Time Trend is statistically significant.

Question 2

A simple method for determining whether autocorrelation is present in a given data set is to

		construct a histogram.
		calculate the variance of the sample.
		examine the residual plot.
		plot the data points from smallest to largest.

Question 3

If positive autocorrelation is not present, then the Durbin-Watson test statistic will be

		close to 2.
		close to 4.
		close to 0.
		greater than 3

Question 4

Heteroskedasticity is a problem because it results in

		biased parameter estimates.
		estimated standard errors that are incorrect.
		estimated standard errors that are always too small.
		incorrect estimated slope coefficients.

Question 5

A given time-series is said to have a time-trend if

		an unexpected shift in time-series data.
		binary dummy variable indicating a time-trend
		the data trend upward or downward over time .
		an independent variable is correlated with the dependent variable but there is no theoretical justification for the relationship.

Question 6

Omitted variable bias occurs when one does not include

		an independent variable that is correlated with the dependent variable only.
		an independent variable that is correlated with the dependent variable and an included independent variable.
		an independent variable that is correlated with an included independent variable only.
		a dependent variable that is correlated with an included independent variable.

Question 7

You can control for a potential time-trend in your data by including a _____ in your regression.

		variable that increases by 1 for each successive time-period
		binary dummy variable indicating a time-trend
		lagged dependent variable
		variable indicating the current time-period

Question 8

Suppose that you plot the residuals from a regression of GDP on the unemployment rate and you get the following

You would conclude that the error terms are

		definitely autocorrelated.
		likely not autocorrelated.
		possibly autocorrelated and you would perform a formal test for autocorrelation.
		possibly autocorrelated and you would perform a correction for heteroskedasticity.

Question 9

Suppose you regress Ice Cream Sales on the number of children under age 10 and on binary dummy variables indicating the 2nd, 3rd, and 4th quarters of the year and you get (p-values in parentheses)

You should conclude that, holding all other independent variables constant, ice cream sales are statistically greater in

		Q1 than in Q4.
		Q1 than in Q3.
		Q4 than in Q2.
		Q2 than in Q1.

Question 10

You can test for a structural break in time-series data by

			including a dummy variable for data after the suspected break and interaction terms between that variable and the remaining independent variables and testing for the joint significance of those terms.
			including dummy variables for three of the four quarters and testing for the joint significance of those variables.
			estimating the regression both with and without the suspect independent variable and comparing the R-squared for the two regressions.
			including a time-trend and testing for the individual significance of that term.

Question 11

The null hypothesis for testing for the presence of autocorrelation is

		the error terms are correlated over time.
		the error terms are not correlated over time.
		the error terms follow an AR(1) process.
		the error terms have constant variance over time.

Question 12

Suppose you estimate restaurant sales as a function of the quality of SERVICE, PRICE, and consumer INCOME and you get the following results (p-values in parentheses)

If the level of statistical significance is set at 10%, we would conclude that

		SERVICE, PRICE, and INCOME are all statistically significant.
		INCOME and SERVICE are statistically significant; PRICE is marginally significant.
		INCOME is statistically significant; SERVICE and PRICE are marginally significant.
		INCOME is statistically significant; SERVICE is marginally significant; PRICE is statistically insignificant.

Question 13

Autocorrelation is a problem because it causes the

		estimated slope coefficients to be biased.
		estimated standard errors to be incorrect.
		data to be spuriously correlated.
		estimated standard errors to always be too small.

Question 14

Suppose that you regress obesity rates on smoking rates for the years 1928-2011 by the model

You have just estimated a _______ model.

		distributed lagged
		time-trend
		seasonality
		time-series econometric

Question 15

White’s Heteroskedastic standard errors are

		the preferred method for correcting for potential heteroskedasticity.
		calculated through an iterative process.
		automatically calculated in Excel.
		the result of performing weighted least squares.

Question 16

A simple way to generate some idea whether data are likely to be heteroskedastic is to

		examine the residual plot.
		construct a histogram.
		calculate the variance of the sample.
		plot the data points from smallest to largest.

Question 17

Suppose that you estimate the sample regression function

After reviewing the results, you might suspect that the marginal effect of

		Experience is estimated incorrectly because it does not seem reasonable that each additional year of experience increases salary by 6.2 percent, holding all other independent constant.
		Education is estimated incorrectly because it does not seem reasonable that each additional year of education increases salary by 3.8 percent, holding all other independent constant.
		having Blue Eyes is estimated incorrectly because it does not seem reasonable that the average salary of individuals with Blue Eyes is 853.8 percent less than the average salary of individuals with other eye colors, holding all other independent constant.
		GPA is estimated incorrectly because it does not seem reasonable that each one unit increase in GPA increases salary by 1.9 percent, holding all other independent constant.

Question 18

The autoregressive structure of the error term is the current-period error term and

		the dependent variable.
		the independent variables.
		prior-period error terms.
		future-period error terms.

Question 19

Seasonality occurs when

		time-series data move upward or downward over time.
		an unexpected shift occurs in time-series data.
		an independent variable is correlated with the dependent variable but there is no theoretical justification for the relationship.
		time-series data follows similar patterns during specific seasons of the year.

Question 20

You can perform forecasting by

		making an educated guess as to what the value of the dependent variable will be at some point in the future.
		regression future dependent variables of future independent variables.
		using the results of regression analysis to predict the value of the dependent variable will be at some point in the future.
		using the results of regression analysis to predict the value of the dependent variable in a past period and comparing the predicted value to the actual value

Question 21

Suppose that you estimate the sample regression function

You might be concerned that the coefficient on experience is a biased estimate of the marginal effect of experience on salary because

		a person’s sex is likely an irrelevant independent variable.
		marital status is likely an irrelevant independent variable.
		education is likely an omitted independent variable.
		the identity of the last NCAA basketball champion is likely an omitted independent variable.

Question 22

The first step of the Durbin-Watson test for the presence of autocorrelation is to estimate the model and determine

		the current period residuals.
		the residuals lagged one period.
		the current period residuals and the residuals lagged one period.
		the current period residuals, the residuals lagged one period, and the residuals lagged two periods.

Question 23

Autocorrelation occurs when

		an omitted independent variable is correlated with the error term.
		the error term is correlated across different time-periods.
		the error term has a non-constant variance.
		the error term is, on average, equal to zero.

Question 24

Weighted Least Squares is performed by

		re-weighting the estimated standard errors from the OLS regression.
		re-weighting the estimated slope coefficients from the OLS regression.
		including the command “,robust” in the estimation.
		re-weighting the original data so that OLS provides estimated standard errors with minimum variance.

Question 25

If autocorrelation is not present, then the Durbin-Watson test statistic will be

		near 0.
		near 2
		near 4
		between 0 and 1

Question 26

Time-series data are data collected for a

		given individual for one time-period.
		given individual or individuals for a number of different time-periods.
		number of individuals for one time-period.
		number of individuals for a number of different time-periods.

Question 27

Suppose that you plot the residuals for your sample against independent variable and get

You should conclude that the data are

		definitely heteroskedastic.
		likely homoskedastic.
		possibly heteroskedastic and you would perform a formal test for heteroskedasticity.
		possibly homoskedastic and you would perform a correction for homoskedasticity.

Question 28

Heteroskedasticity occurs when

		the error variance is constant.
		the error variance is non-constant.
		the dependent variable variance is constant.
		the dependent variable variance is non-constant.

Question 29

Suppose that you are performing the Regression test for AR(1) and you get (standard errors in parentheses) with 50 observations

You would conclude that

		autocorrelation is not present in the data.
		autocorrelation is present in the data.
		heteroskedasticity is not present in the data.
		heteroskedasticity is present in the data.

Question 30

Omitted variable bias is a potential problem because it

		prevents accurately estimating true marginal effects.
		results in estimated standard errors that are too large.
		results in inefficient parameter estimates.
		might highlight spurious correlations.

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