Econometric 4-5-6-7-8

Frage 1 von 26

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Binary variables

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are generally used to control for outliers in your sample.
can take on more than two values.
exclude certain individuals from your sample.
can take on only two values.

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Frage 2 von 26

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In the simple linear regression model, the regression slope

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indicates by how many percent Y increases, given a one percent increase in X.
when multiplied with the explanatory variable will give you the predicted Y.
indicates by how many units Y increases, given a one unit increase in X.
represents the elasticity of Y on X.

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Frage 3 von 26

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In which of the following relationships does the intercept have a real-world interpretation?

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the relationship between the change in the unemployment rate and the growth rate of real GDP (“Okun’s Law”)
the demand for coffee and its price
test scores and class-size
weight and height of individuals

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Frage 4 von 26

1

The OLS residuals, ˆi u , are sample counterparts of the population

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regression function slope
errors
regression function’s predicted values
regression function intercept

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Frage 5 von 26

1

Changing the units of measurement, e.g. measuring test scores in 100s, will do all of the following EXCEPT for changing the

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residuals
numerical value of the slope estimate
interpretation of the effect that a change in X has on the change in Y
numerical value of the intercept

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Frage 6 von 26

1

To decide whether the slope coefficient indicates a “large” effect of X on Y, you look at the

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size of the slope coefficient
regression R2
economic importance implied by the slope coefficient
value of the intercept

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Frage 7 von 26

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The t-statistic is calculated by dividing

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the OLS estimator by its standard error.
the slope by the standard deviation of the explanatory variable.
the estimator minus its hypothesized value by the standard error of the
estimator.
the slope by 1.96.

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Frage 8 von 26

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A binary variable is often called a

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dummy variable
dependent variable
residual
power of a test

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Frage 9 von 26

1

If the errors are heteroskedastic, then

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OLS is BLUE
WLS is BLUE if the conditional variance of the errors is known up to a constant factor of proportionality
LAD is BLUE if the conditional variance of the errors is known up to a constant factor of proportionality
OLS is efficient

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Frage 10 von 26

1

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

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use the homoskedasticity only formula because the t-statistic becomes larger
first test for homoskedasticity of the errors and then make a decision
use the heteroskedasticity robust formula
make a decision depending on how much different the estimate of the slope is under the two procedures

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Frage 11 von 26

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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:

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you decide that the coefficient is small and hence most likely is zero in the population
the slope is statistically significant since it is four standard errors away from zero
the response of Y given a change in X must be economically important since it is statistically significant
since the slope is very small, so must be the regression R2(square).

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Frage 12 von 26

1

In the multiple regression model, the adjusted R2, R2

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cannot be negative.
will never be greater than the regression R2(square).
equals the square of the correlation coefficient r.
cannot decrease when an additional explanatory variable is added.

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Frage 13 von 26

1

If you had a two regressor regression model, then omitting one variable which is relevant

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will have no effect on the coefficient of the included variable if the correlation between the excluded and the included variable is negative.
will always bias the coefficient of the included variable upwards.
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.
makes the sum of the product between the included variable and the residuals different from 0.

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Frage 14 von 26

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Under the least squares assumptions for the multiple regression problem (zero conditional mean for the error term, all Xi and Yi being i.i.d., all Xi and ui having finite fourth moments, no perfect multicollinearity), the OLS estimators for the slopes and intercept

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have an exact normal distribution for n > 25.
are BLUE.
have a normal distribution in small samples as long as the errors are homoskedastic.
are unbiased and consistent.

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Frage 15 von 26

1

The following OLS assumption is most likely violated by omitted variables bias:

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there is heteroskedasticity

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Frage 16 von 26

1

The dummy variable trap is an example of

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imperfect multicollinearity
something that is of theoretical interest only
perfect multicollinearity
something that does not happen to university or college students

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Frage 17 von 26

1

Imperfect multicollinearity

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is not relevant to the field of economics and business administration
only occurs in the study of finance
means that the least squares estimator of the slope is biased
means that two or more of the regressors are highly correlated

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Frage 18 von 26

1

Consider the multiple regression model with two regressors X1 and X2, where both variables are determinants of the dependent variable. You first regress Y on X1 only and find no relationship. However when regressing Y on X1 and X2, the slope coefficient 1ˆ changes by a large amount. This suggests that your first regression suffers from

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heteroskedasticity
perfect multicollinearity
omitted variable bias
dummy variable trap

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Frage 19 von 26

1

Imperfect multicollinearity

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implies that it will be difficult to estimate precisely one or more of the partial effects using the data at hand
violates one of the four Least Squares assumptions in the multiple regression model
means that you cannot estimate the effect of at least one of the Xs on Y
suggests that a standard spreadsheet program does not have enough power to estimate the
multiple regression model

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Frage 20 von 26

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When testing joint hypothesis, you should

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use t-statistics for each hypothesis and reject the null hypothesis is all of the restrictions fail
use the F-statistic and reject all the hypothesis if the statistic exceeds the critical value
use t-statistics for each hypothesis and reject the null hypothesis once the statistic exceeds the critical value for a single hypothesis
use the F-statistics and reject at least one of the hypothesis if the statistic exceeds the critical value

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Frage 21 von 26

1

In the multiple regression model, the t-statistic for testing that the slope is significantly different from zero is calculated

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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(square) and the confidence interval.

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Frage 22 von 26

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If you wanted to test, using a 5% significance level, whether or not a specific slope coefficient is equal to one, then you should

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subtract 1 from the estimated coefficient, divide the difference by the standard error, and check if the resulting ratio is larger than 1.96.
add and subtract 1.96 from the slope and check if that interval includes 1.
see if the slope coefficient is between 0.95 and 1.05.
check if the adjusted R2 is close to 1.

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Frage 23 von 26

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When there are two coefficients, the resulting confidence sets are

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rectangles
ellipses
squares
trapezoids

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Frage 24 von 26

1

The homoskedasticity-only F-statistic and the heteroskedasticity-robust F-statistic typically are

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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)

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Frage 25 von 26

1

A nonlinear function

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makes little sense, because variables in the real world are related linearly.
can be adequately described by a straight line between the dependent variable and one of the explanatory variables.
is a concept that only applies to the case of a single or two explanatory variables since you cannot draw a line in four dimensions.
is a function with a slope that is not constant.

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Frage 26 von 26

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The best way to interpret polynomial regressions is to

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take a derivative of Y with respect to the relevant X.
plot the estimated regression function and to calculate the estimated effect on Y associated with a change in X for one or more values of X.
look at the t-statistics for the relevant coefficients.
analyze the standard error of estimated effect.

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