Regression Analysis: A Comprehensive Guide for Economics Students

Question 1

In a simple linear regression model, the dependent variable is a linear function of:

Accepted Answer

Both the intercept and the slope coefficient

Answer

Only the intercept

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Only the slope coefficient

Answer

The error term

Question 2

In multiple regression, the t-test for individual coefficients determines whether:

Accepted Answer

The coefficient is statistically significant from zero

Answer

The coefficient is significantly different from another coefficient

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The coefficient is positive

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The coefficient is negative

Question 3

Heteroscedasticity refers to:

Accepted Answer

Non-constant variance of the error term

Answer

Constant variance of the error term

Answer

Non-zero mean of the error term

Answer

Correlation between the error term and independent variables

Question 4

Multicollinearity occurs when:

Accepted Answer

Two or more independent variables are highly correlated

Answer

The dependent variable is correlated with the error term

Answer

The error term is not normally distributed

Answer

The sample size is insufficient

Question 5

What is the primary objective of using a residual plot in regression analysis?

Accepted Answer

To identify patterns in the residuals

Answer

To test the assumptions of the regression model

Answer

To select the best model among several candidates

Question 6

What is the main purpose of using cross-validation in regression analysis?

Accepted Answer

To evaluate the predictive accuracy of a model

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To handle missing data

Answer

To identify influential observations

Question 7

What does the intercept in a regression model represent?

Accepted Answer

The value of the dependent variable when all independent variables are zero.

Answer

The adjustment for outliers in the data.

Answer

The effect of an additional unit of an independent variable on the dependent variable.

Answer

The statistical significance of the model.

Question 8

What is the primary purpose of a residual plot?

Accepted Answer

To check for the presence of outliers and non-linear relationships.

Answer

To estimate the coefficients of the regression model.

Answer

To predict the value of the dependent variable for a given set of independent variables.

Answer

To determine the level of statistical significance of the model.

Question 9

In a t-test for the significance of a regression coefficient, what is the null hypothesis?

Accepted Answer

The coefficient is equal to zero.

Answer

The coefficient is not equal to zero.

Answer

The coefficient is greater than zero.

Answer

The coefficient is less than zero.

Question 10

What is the purpose of a confidence interval for a regression coefficient?

Accepted Answer

To provide a range of values within which the true value of the coefficient is likely to fall.

Answer

To test the statistical significance of the coefficient.

Answer

To predict the value of the dependent variable for a given set of independent variables.

Answer

To adjust for the presence of multicollinearity.

Question 11

What is the difference between a dummy variable and a continuous variable?

Accepted Answer

A dummy variable takes on only two values, while a continuous variable can take on any value.

Answer

A continuous variable takes on only two values, while a dummy variable can take on any value.

Answer

A dummy variable is a type of independent variable, while a continuous variable is a type of dependent variable.

Answer

A continuous variable is a type of independent variable, while a dummy variable is a type of dependent variable.

Question 12

What is the purpose of a scatterplot in regression analysis?

Accepted Answer

To visualize the relationship between the dependent and independent variables.

Answer

To estimate the parameters of the regression model.

Answer

To predict the value of the dependent variable for a given value of the independent variable.

Answer

To determine if the regression model is statistically significant.

Question 13

The Durbin-Watson statistic is used to test for:

Accepted Answer

Serial correlation in the error term

Answer

Heteroscedasticity in the error term

Answer

Non-linearity in the relationship between the dependent and independent variables

Answer

Multicollinearity between the independent variables

Question 14

In a regression model with two independent variables, which of the following would indicate a positive relationship between the first independent variable and the dependent variable?

Accepted Answer

A positive coefficient for the first independent variable

Answer

A negative coefficient for the first independent variable

Answer

A coefficient of zero for the first independent variable

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A positive coefficient for the second independent variable

Question 15

In a scatterplot, a strong positive correlation between two variables would be represented by:

Accepted Answer

Points that form a straight line with a positive slope

Answer

Points that form a straight line with a negative slope

Answer

Points that are randomly scattered

Answer

Points that form a circle

Question 16

What is the main difference between simple and multiple regression models?

Accepted Answer

Simple regression models have a single independent variable, while multiple regression models have two or more independent variables.

Answer

Multiple regression models are more accurate than simple regression models.

Answer

Multiple regression models can only be used with continuous variables, while simple regression models can be used with both continuous and categorical variables.

Answer

Simple regression models are easier to interpret than multiple regression models.

Question 17

What is the purpose of the coefficient of determination (R-squared) in regression analysis?

Accepted Answer

To measure the proportion of variation in the dependent variable that is explained by the independent variables.

Answer

To test the significance of the regression model.

Answer

To predict the value of the dependent variable for a given set of independent variables.

Answer

To determine the direction of the relationship between the dependent and independent variables.

Question 18

In a simple linear regression model, what does the coefficient of determination (R-squared) represent?

Accepted Answer

The proportion of the variation in the dependent variable explained by the independent variable.

Answer

The total variation in the dependent variable.

Answer

The slope of the regression line.

Answer

The strength of the linear relationship between the variables.

Question 19

A regression model was estimated with the following equation: Y = 20 + 5X.  What is the predicted value of Y when X equals 10?

Accepted Answer

70

Answer

50

Answer

25

Answer

30

Question 20

A statistically significant coefficient in a regression model suggests that:

Accepted Answer

The independent variable has a statistically significant effect on the dependent variable, holding other variables constant.

Answer

There is no relationship between the independent and dependent variables.

Answer

The model is a perfect fit for the data.

Answer

The independent variable is the sole factor influencing the dependent variable.

Question 21

Which of the following is a common method for identifying multicollinearity in a multiple regression model?

Accepted Answer

Calculating the Variance Inflation Factor (VIF).

Answer

Examining the p-values of the regression coefficients.

Answer

Plotting the residuals against the predicted values.

Answer

Performing a Durbin-Watson test.

Question 22

Heteroscedasticity in regression analysis refers to:

Accepted Answer

Non-constant variance of the error terms across different values of the independent variable.

Answer

Non-linear relationship between the dependent and independent variables.

Answer

Presence of outliers in the data.

Answer

Correlation between the error terms and the independent variables.

Question 23

Which of the following techniques can be employed to address the problem of heteroscedasticity?

Accepted Answer

Using weighted least squares regression.

Answer

Transforming the dependent variable only.

Answer

Adding more independent variables to the model.

Answer

Removing outliers from the data.

Question 24

In a multiple regression model, a high adjusted R-squared value indicates that:

Accepted Answer

The model explains a large proportion of the variation in the dependent variable, taking into account the number of independent variables.

Answer

The model is a perfect fit for the data.

Answer

The model is free from multicollinearity.

Answer

The model has a low standard error of estimate.

Question 25

What is the primary purpose of using dummy variables in regression analysis?

Accepted Answer

To incorporate categorical variables (with more than two categories) into the regression model.

Answer

To handle missing data in the independent variables.

Answer

To transform non-linear relationships into linear ones.

Answer

To increase the overall R-squared value of the model.

Question 26

Which of the following statements accurately describes the Ordinary Least Squares (OLS) method of estimation in regression analysis?

Accepted Answer

OLS minimizes the sum of squared differences between the observed and predicted values of the dependent variable.

Answer

OLS is not sensitive to outliers in the data.

Answer

OLS requires the error terms to be normally distributed.

Answer

OLS always produces the most accurate regression model.