Deck 6: Multiple Regression Analysis: Further Issues

Question 1

Which of the following correctly identifies an advantage of using adjusted R² over R²?

A)Adjusted R² corrects the bias in R².
B)Adjusted R² is easier to calculate than R².
C) The penalty of adding new independent variables is better understood through adjusted R² than R².
D) The adjusted R² can be calculated for models having logarithmic functions while R² cannot be calculated for such models.

Answer 1

C
Explanation: The penalty of adding new independent variables is better understood through adjusted R² than R² since its calculation is directly dependent on the number of independent variables included.

Question 2

Standardized coefficients are also referred to as:

A)beta coefficients.
B)y coefficients.
C) alpha coefficients.
D) j coefficients.

Answer 2

A
Explanation: Standardized coefficients are also referred to as beta coefficients.

Question 3

Two equations form a nonnested model when:

A)one is logarithmic and the other is quadratic.
B)neither equation is a special case of the other.
C) each equation has the same independent variables.
D) there is only one independent variable in both equations.

Answer 3

B
Explanation: Two equations form a nonnested model when neither equation is a special case of the other.

Question 4

Residual analysis refers to the process of:

A)examining individual observations to see whether the actual value of a dependent variable differs from the predicted value.
B)calculating the squared sum of residuals to draw inferences for the consistency of estimates.
C) transforming models with variables in level to logarithmic functions so as to understand the effect of percentage changes in the independent variable on the dependent variable.
D) sampling and collection of data in such a way to minimize the squared sum of residuals.

Question 5

In the following equation, gdp refers to gross domestic product, and FDI refers to foreign direct investment. ​
Log(gdp) = 2.65 + 0.527log(bankcredit) + 0.222FDI
(0)13) (0.022) (0.017)
​
Which of the following statements is then true?

A)If gdp increases by 1%, bank credit increases by 0.527%, the level of FDI remaining constant.
B)If bank credit increases by 1%, gdp increases by 0.527%, the level of FDI remaining constant.
C) If gdp increases by 1%, bank credit increases by log(0.527)%, the level of FDI remaining constant.
D) If bank credit increases by 1%, gdp increases by log(0.527)%, the level of FDI remaining constant.

Question 6

If we use to estimate ​, then the residual for predicting yi is:

A)​
B)​
C) ​

D) ​

Question 7

A variable is standardized in the sample:

A)by multiplying by its mean.
B)by subtracting off its mean and multiplying by its standard deviation.
C) by subtracting off its mean and dividing by its standard deviation.
D) by multiplying by its standard deviation.

Question 8

Which of the following correctly represents the equation for adjusted R²?

A) = 1 - [SSR/(n -1)]/[SST/(n+1)]
B) = 1 - [SSR/(n -k - 1)]/[SST/(n+1)]
C)
= 1 - [SSR/(n -k - 1)]/[SST/(n - 1)]
D)
= 1 - [SSR]/[SST/(n - 1)]

Question 9

One popular measure to describe the relationship between the dependent variable y and each explanatory variable is the:

A)​standardized effect.
B)​interaction effect.
C) ​average partial effect.
D) ​partial effect.

Question 10

In the following equation, gdp refers to gross domestic product, and FDI refers to foreign direct investment. log(gdp) = 2.65 + 0.527log(bankcredit) + 0.222FDI
(0)13) (0.022) (0.017)
​
Which of the following statements is then true?

A)If FDI increases by 1%, gdp increases by approximately 22.2%, the amount of bank credit remaining constant.
B)If FDI increases by 1%, gdp increases by approximately 26.5%, the amount of bank credit remaining constant.
C) If FDI increases by 1%, gdp increases by approximately 24.8%, the amount of bank credit remaining constant.
D) If FDI increases by 1%, gdp increases by approximately 52.7%, the amount of bank credit remaining constant.

Question 11

Changing the unit of measurement of any independent variable, where log of the dependent variable appears in the regression:

A)affects only the intercept coefficient.
B)affects only the slope coefficient.
C) affects both the slope and intercept coefficients.
D) affects neither the slope nor the intercept coefficient.

Question 12

If a regression equation has only one explanatory variable, say x₁, its standardized coefficient must lie in the range:

A)-2 to 0.
B)-1 to 1.
C) 0 to 1.
D) 0 to 2.

Question 13

Which of the following correctly identifies a limitation of logarithmic transformation of variables?

A)Taking log of variables make OLS estimates more sensitive to extreme values in comparison to variables taken in level.
B)Logarithmic transformations cannot be used if a variable takes on zero or negative values.
C) Logarithmic transformations of variables are likely to lead to heteroskedasticity.
D) Taking log of a variable often expands its range which can cause inefficient estimates.

Question 14

A predicted value of a dependent variable:

A)represents the difference between the expected value of the dependent variable and its actual value.
B)is always equal to the actual value of the dependent variable.
C) is independent of explanatory variables and can be estimated on the basis of the residual error term only.
D) represents the expected value of the dependent variable given particular values for the explanatory variables.

Question 15

The centering of explanatory variables about their sample averages before creating quadratics or interactions forces the coefficient on the levels to be average partial effects.​

Question 16

Beta coefficients are always greater than standardized coefficients.

Question 17

A change in the unit of measurement of the dependent variable in a model does not lead to a change in:

A)the standard error of the regression.
B)the sum of squared residuals of the regression.
C) the goodness-of-fit of the regression.
D) the confidence intervals of the regression.

Question 18

Which of the following statements is true when the dependent variable, y > 0?

A)Taking log of a variable often expands its range.
B)Models using log(y) as the dependent variable will satisfy CLM assumptions more closely than models using the level of y.
C) Taking log of variables make OLS estimates more sensitive to extreme values.
D) Taking logarithmic form of variables make the slope coefficients more responsive to rescaling.

Question 19

Which of the following models is used quite often to capture decreasing or increasing marginal effects of a variable?

A)Models with logarithmic functions
B)Models with quadratic functions
C) Models with variables in level
D) Models with interaction terms

Question 20

An independent variable can be included in a regression model:​

A)​when it affects y and is uncorrelated with all of the independent variables of interest.
B)​when it does not affect y and is uncorrelated with all of the independent variables of interest.
C) ​when it affects y and is correlated with all of the independent variables of interest.
D) ​when it does not affect y and is correlated with all of the independent variables of interest.

Question 21

To make predictions of logarithmic dependent variables, they first have to be converted to their level forms.

Question 22

If a new independent variable is added to a regression equation, the adjusted R² increases only if the absolute value of the t statistic of the new variable is greater than one.

Question 23

Predictions of a dependent variable are subject to sampling variation.

Question 24

If the R-squared value is low, then using OLS equation is very easy to predict individual future outcomes on y given a set of values for the explanatory variables.​

Question 25

F statistic can be used to test nonnested models.