Assumptions of Regression Analysis: Master the Foundations of Econometrics

Question 1

What is the purpose of a residual plot?

Accepted Answer

To check for the factors listed in (a)-(c).

Answer

To check for linearity (i.e., constant variance).

Answer

To check for homoscedasticity (i.e., non-random pattern).

Answer

To check for independence of errors (i.e., no correlation).

Question 2

Which of the following scenarios violates the assumption of homoscedasticity in regression analysis?

Accepted Answer

Residuals have varying variance as the independent variable's value changes.

Answer

Residuals have constant variance across all values of the independent variable.

Answer

Residuals are randomly scattered around the regression line, forming a uniform band.

Answer

Residuals are strongly correlated with the independent variable, exhibiting a distinct pattern.

Question 3

Which of the following statements represents an assumption of simple linear regression analysis?

Accepted Answer

Errors are independent of each other

Answer

The relationship between the dependent and independent variables is non-linear

Answer

The variance of the errors is increasing

Answer

Errors are linearly distributed

Question 4

Homoscedasticity refers to the assumption that:

Accepted Answer

The variance of the errors is constant

Answer

The errors are normally distributed

Answer

The errors are independent of each other

Answer

The relationship between the dependent and independent variables is linear

Question 5

What is a consequence of violating the assumption of independence of errors?

Accepted Answer

The OLS estimator will be inefficient

Answer

The OLS estimator will be consistent

Answer

The OLS estimator will be biased

Question 6

What is the primary purpose of testing the assumptions of regression analysis?

Accepted Answer

To ensure the validity and reliability of the regression results

Answer

To identify outliers in the data

Answer

To determine the best model to use

Question 7

Which statistical test is specifically designed to test for homoscedasticity?

Accepted Answer

Breusch-Pagan test

Answer

Kolmogorov-Smirnov test

Answer

Durbin-Watson test

Answer

Jarque-Bera test

Question 8

What is the primary purpose of using diagnostic plots in regression analysis?

Accepted Answer

To identify violations of the assumptions of regression analysis

Answer

To calculate the standard error of the regression

Answer

To determine the best model to use

Question 9

Which of the following is a fundamental assumption of regression analysis?

Accepted Answer

Linearity between the dependent variable and the independent variables

Answer

Autocorrelation in the error term

Answer

Heteroscedasticity in the error term

Answer

Nonlinearity between the dependent variable and the independent variables

Question 10

Homoscedasticity in regression analysis implies that:

Accepted Answer

The variance of the error term is constant for all values of the independent variables.

Answer

The error term is independent of the independent variables.

Answer

The expected value of the error term is zero.

Answer

The error term is normally distributed.

Question 11

Violating the assumption of independence of errors in regression analysis can result in:

Accepted Answer

Biased regression coefficients

Answer

Efficient regression coefficients

Answer

Consistent regression coefficients

Question 12

The primary purpose of the Durbin-Watson test in regression analysis is to:

Accepted Answer

Detect autocorrelation in the error term

Answer

Assess normality of the error term

Answer

Test for multicollinearity among the independent variables

Answer

Identify heteroscedasticity in the error term

Question 13

Which of the following is an appropriate method for detecting multicollinearity in regression analysis?

Accepted Answer

Variance Inflation Factor (VIF)

Answer

Breusch-Pagan test

Answer

Jarque-Bera test

Answer

Durbin-Watson test

Question 14

Violating the assumption of normality in the error term of regression analysis can potentially lead to:

Accepted Answer

Invalidity of the t-test and F-test statistics for hypothesis testing

Answer

Biased regression coefficients

Answer

Inflated standard errors of the regression coefficients

Question 15

Which of the following is NOT a valid assumption of regression analysis?

Accepted Answer

Perfect correlation among the independent variables

Answer

Zero mean error term

Answer

Linear relationship between the dependent variable and the independent variables

Question 16

What is the difference between multicollinearity and autocorrelation?

Accepted Answer

Multicollinearity refers to correlation among independent variables, while autocorrelation refers to correlation among error terms

Answer

Multicollinearity affects the standard errors of the coefficients, while autocorrelation affects the hypothesis tests

Question 17

What is the purpose of using a log transformation in regression analysis?

Accepted Answer

To linearize a non-linear relationship or to stabilize the variance of the error terms

Answer

To improve the predictive accuracy of the model

Answer

To reduce the standard error of the estimates

Question 18

Which of the following assumptions is particularly important for causal inference using regression analysis?

Accepted Answer

Exogeneity

Answer

Linearity

Answer

Normality

Answer

Homoscedasticity

Question 19

What is the role of residual analysis in assessing regression assumptions?

Accepted Answer

To detect patterns or outliers that may indicate violations of assumptions

Answer

To test the significance of individual variables

Answer

To calculate the standard errors of the coefficients

Question 20

Which of the following is NOT an assumption of the Gauss-Markov theorem?

Accepted Answer

The error term has a non-zero mean

Answer

The error terms have a constant variance

Answer

The error terms are independent and normally distributed

Answer

The regressors are fixed and exogenous

Question 21

In a regression model, the assumption of homoscedasticity implies that:

Accepted Answer

The variance of the error term is constant across all observations

Answer

The error terms are uncorrelated

Answer

The mean of the error term is zero

Question 22

The assumption of linearity in regression analysis implies that:

Accepted Answer

The relationship between the dependent variable and independent variables is linear

Answer

The regressors are independent of the dependent variable

Answer

The error term has a normal distribution

Question 23

Which of the following is a diagnostic test for homoscedasticity?

Accepted Answer

Breusch-Pagan test

Answer

Jarque-Bera test

Answer

White test

Answer

Durbin-Watson test

Question 24

The assumption of multicollinearity refers to:

Accepted Answer

High correlation among independent variables

Answer

Non-linear relationship between variables

Answer

Heteroscedasticity

Answer

Non-random distribution of errors

Question 25

Which of the following is NOT a potential consequence of multicollinearity?

Accepted Answer

Improved prediction accuracy

Answer

Increased standard errors of parameter estimates

Answer

Inconsistent parameter estimates

Answer

Instability of parameter estimates

Question 26

The Durbin-Watson test is used to test for:

Accepted Answer

Autocorrelation

Answer

Multicollinearity

Answer

Linearity

Answer

Heteroscedasticity

Question 27

What are the consequences of violating the homoscedasticity assumption in regression analysis?

Accepted Answer

Heteroscedasticity, leading to biased standard errors.

Answer

Serial correlation, leading to biased parameter estimates.

Answer

Multicollinearity, leading to unstable parameter estimates.

Question 28

What are the potential impacts of serial correlation on regression analysis?

Accepted Answer

Biased parameter estimates and inflated standard errors.

Answer

Unbiased parameter estimates, but reduced statistical power.

Answer

Biased parameter estimates, but reduced standard errors.

Question 29

What is the primary purpose of using a scatterplot in regression analysis?

Accepted Answer

To visually assess the linearity and homoscedasticity of the relationship between the variables.

Answer

To estimate the parameters of the regression equation.

Answer

To test the significance of the independent variables.

Question 30

Which of the following is a measure of the goodness-of-fit of a regression model that adjusts for the number of independent variables?

Accepted Answer

Adjusted R-squared

Answer

Jarque-Bera statistic

Answer

Coefficient of determination

Answer

Durbin-Watson statistic

Question 31

What are the key differences between a statistical model and a practical model in regression analysis?

Accepted Answer

A statistical model emphasizes predictive accuracy, while a practical model balances predictive accuracy with interpretability and parsimony.

Answer

A statistical model uses only quantitative data, while a practical model can also use qualitative data.

Question 32

Which of the following is a common cause of multicollinearity in regression analysis?

Accepted Answer

When two or more independent variables are highly correlated with each other.

Answer

When the dependent variable is not normally distributed.

Answer

When the sample size is too small.

Question 33

Which of the following is NOT a core assumption of the Gauss-Markov theorem?

Accepted Answer

The dependent variable is normally distributed.

Answer

The error term has constant variance (homoscedasticity).

Answer

The relationship between the dependent and independent variables is linear.

Answer

The independent variables are uncorrelated with the error term.

Question 34

What is the consequence of violating the assumption of homoscedasticity?

Accepted Answer

The OLS estimators will be inefficient

Answer

The OLS estimators will not be normally distributed

Answer

The OLS estimators will be biased

Question 35

What is the purpose of the Durbin-Watson statistic?

Accepted Answer

To test for autocorrelation in the error term

Answer

To test for heteroscedasticity

Answer

To test for normality of the error term

Answer

To test for multicollinearity

Question 36

What are the consequences of multicollinearity?

Accepted Answer

All of the below

Answer

The OLS estimators will be inefficient

Answer

The OLS estimators will be biased

Answer

The OLS estimators will have a larger variance

Question 37

What is the purpose of a confidence interval?

Accepted Answer

To estimate the true value of a parameter

Answer

To predict future values of a variable

Answer

To determine the significance of a relationship between variables

Answer

To test hypotheses about a parameter

Question 38

Which assumption of linear regression directly implies that the relationship between the independent and dependent variables can be represented by a straight line?

Accepted Answer

Linearity

Answer

Homoscedasticity

Answer

Independence of errors

Question 39

If a scatterplot of residuals against predicted values shows a clear pattern, like a funnel shape, which assumption of regression is likely being violated?

Accepted Answer

Homoscedasticity

Answer

Linearity

Answer

Independence of errors

Question 40

The Durbin-Watson statistic is primarily used to test for:

Accepted Answer

Autocorrelation of errors

Answer

Non-normality of errors

Answer

Multicollinearity

Answer

Heteroscedasticity

Question 41

If the errors in a regression model are not normally distributed, which of the following is NOT a direct consequence?

Accepted Answer

The regression coefficients will be biased.

Answer

Hypothesis tests may be unreliable.

Answer

Predictions may be less precise.

Answer

Confidence intervals may be inaccurate.

Question 42

Which of the following techniques is commonly used to address the problem of multicollinearity in regression analysis?

Accepted Answer

Variable selection

Answer

Increasing sample size

Answer

Transforming variables

Answer

Adding more independent variables

Question 43

A researcher observes that the variability of the error terms seems to change as the independent variable changes. Which assumption of regression analysis is likely being violated?

Accepted Answer

Homoscedasticity

Answer

Linearity

Answer

Independence of errors

Answer

Normality of errors

Question 44

In a time series regression, the assumption of independence of errors is violated when:

Accepted Answer

Errors in one period are correlated with errors in previous periods.

Answer

The independent variable is correlated with the error term.

Answer

The error term is not normally distributed.

Question 45

If the assumption of normality of errors is violated in a regression model, what can be done to improve the robustness of the analysis?

Accepted Answer

Use robust standard errors or consider non-parametric methods.

Answer

Remove outliers from the data.

Answer

Increase the sample size.

Question 46

Which of the following is NOT always a direct consequence of violating the assumptions of regression analysis?

Accepted Answer

The regression coefficients will always be biased.

Answer

Confidence intervals may be inaccurate.

Answer

Predictions may be less precise.

Answer

Hypothesis tests may be unreliable.

Question 47

A researcher wants to use regression analysis to model the relationship between income and education level.  Which of the following assumptions should be carefully considered before proceeding?

Accepted Answer

All of the above.

Answer

Independence of errors

Answer

Linearity

Answer

Homoscedasticity

Question 48

Which of the following is an assumption of regression analysis?

Accepted Answer

Linearity

Answer

Normality

Answer

All variables are categorical

Question 49

Homoscedasticity refers to the assumption that:

Accepted Answer

The variance of the errors is constant

Answer

The dependent variable is continuous

Answer

The errors are normally distributed

Answer

The independent variables are not correlated

Question 50

Which of the following is a consequence of violating the assumption of independence of errors?

Accepted Answer

Biased standard errors

Answer

Overestimation of the coefficient of determination

Answer

Underestimation of the p-values

Answer

Inconsistent parameter estimates

Question 51

Which of the following plots can be used to assess the assumption of linearity?

Accepted Answer

Scatterplot of the residuals against the fitted values

Answer

Histogram of the residuals

Answer

Normal probability plot of the residuals

Question 52

What is the purpose of the Breusch-Pagan test?

Accepted Answer

To test for heteroscedasticity

Answer

To test for normality

Answer

To test for independence of errors

Answer

To test for multicollinearity

Question 53

Which of the following is a potential consequence of violating the assumption of normality?

Accepted Answer

The t-tests for the individual coefficients may not be valid

Answer

The F-test for the overall significance of the regression will not be valid

Answer

The coefficient of determination will be biased

Question 54

What is the effect of multicollinearity on the regression coefficients?

Accepted Answer

They become less precise

Answer

They become biased

Answer

They become more precise

Answer

They become zero

Question 55

Which of the following is a method for dealing with multicollinearity?

Accepted Answer

Dropping one of the collinear variables

Answer

Using a ridge regression model

Answer

Transforming the independent variables

Answer

Adding more independent variables to the regression

Question 56

What is the Durbin-Watson statistic used to test for?

Accepted Answer

Autocorrelation

Answer

Multicollinearity

Answer

Heteroscedasticity

Answer

Normality

Question 57

Which of the following is NOT an assumption of regression analysis?

Accepted Answer

The independent variables are measured without error

Answer

The relationship between the dependent variable and the independent variables is linear

Answer

The dependent variable is continuous