Regression Analysis Quizzes: Master the Fundamentals of Regression

Question 1

The maximum possible value of the coefficient of determination is:

Accepted Answer

1

Answer

0

Answer

-1

Answer

2

Question 2

In hypothesis testing, a Type I error occurs when:

Accepted Answer

The null hypothesis is true and is rejected

Answer

The null hypothesis is false and is accepted

Answer

The alternative hypothesis is true and is rejected

Answer

The alternative hypothesis is false and is accepted

Question 3

What does the coefficient of determination (R-squared) measure?

Accepted Answer

Proportion of variation in the dependent variable explained by the independent variable.

Answer

Amount of error in the model.

Answer

Strength of the relationship between the variables.

Answer

Slope of the regression line.

Question 4

What is the key difference between a positive and negative correlation?

Accepted Answer

Positive correlation indicates a direct relationship, while negative correlation indicates an inverse relationship.

Answer

Positive correlation indicates an inverse relationship, while negative correlation indicates a direct relationship.

Answer

Positive correlation indicates a relationship, while negative correlation indicates no relationship.

Answer

There is no key difference between positive and negative correlations.

Question 5

Which of the following is NOT a type of regression model?

Accepted Answer

Correlation analysis

Answer

Linear regression

Answer

Logistic regression

Answer

Poisson regression

Question 6

What is the correlation coefficient?

Accepted Answer

A measure of the strength and direction of the linear relationship between two variables.

Answer

A measure of the goodness of fit of a regression model.

Answer

The slope of the regression line.

Answer

The intercept of the regression line.

Question 7

What is the purpose of a scatterplot in regression analysis?

Accepted Answer

To visualize the relationship between the independent and dependent variables.

Answer

To determine the equation of the regression line.

Answer

To calculate the correlation coefficient.

Answer

To predict future values of the dependent variable.

Question 8

The equation of a simple linear regression model is:

Accepted Answer

y = mx + b

Answer

y = mx + c

Answer

y = cx + b

Answer

y = x + b

Question 9

The coefficient of determination (R-squared) indicates:

Accepted Answer

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

Answer

The value of the dependent variable for a given value of the independent variable.

Answer

The direction of the relationship between the dependent and independent variables.

Answer

The significance of the regression model.

Question 10

Which of the following is true about correlation and causation?

Accepted Answer

Causation implies correlation.

Answer

Correlation implies causation.

Answer

Correlation and causation are the same thing.

Answer

Correlation and causation are unrelated concepts.

Question 11

Which type of regression analysis is used to predict categorical dependent variables?

Accepted Answer

Logistic regression

Answer

Linear regression

Answer

Ridge regression

Answer

Lasso regression

Question 12

The purpose of regularisation in regression analysis is:

Accepted Answer

Reduce overfitting.

Answer

Improve predictive accuracy.

Answer

Reduce independent variables.

Answer

Enhance interpretability.

Question 13

In simple linear regression, the dependent variable is **predicted by** the independent variable.

Accepted Answer

Predicted by the independent variable

Answer

Predicts the independent variable

Answer

Independent of the independent variable

Answer

Constant

Question 14

Which of the following is an assumption of simple linear regression? **Normally distributed errors**

Accepted Answer

Normally distributed errors

Answer

Linear relationship between the variables

Answer

Homoscedasticity of errors

Answer

Independence of errors

Question 15

Which of the following is a measure of the variability in the dependent variable that is explained by the regression model? **Sum of squares due to regression**

Accepted Answer

Sum of squares due to regression

Answer

Sum of squares due to error

Answer

Total sum of squares

Answer

Coefficient of determination

Question 16

Which of the following is NOT an assumption of the simple linear regression model?

Accepted Answer

Normally distributed error term

Answer

Linear relationship between the dependent variable and the independent variable

Answer

Independence of observations

Answer

Constant variance of the error term (homoscedasticity)

Question 17

Which of the following is a benefit of using standardized regression coefficients?

Accepted Answer

They make it easier to compare the relative importance of different independent variables.

Answer

They can be used to predict the value of the dependent variable for any value of the independent variable.

Answer

They are more robust to outliers than unstandardized coefficients.

Answer

They can be used to test the significance of individual regression coefficients.

Question 18

In simple linear regression, the slope of the regression line represents the:

Accepted Answer

Change in the dependent variable for a one-unit increase in the independent variable

Answer

Intercept of the regression line

Answer

Coefficient of determination

Answer

Mean of the dependent variable

Question 19

The coefficient of determination (R²) represents the:

Accepted Answer

Proportion of variance in the dependent variable explained by the regression model

Answer

Slope of the regression line

Answer

Strength of the correlation between the variables

Question 20

In multiple regression, the coefficient for an independent variable represents the:

Accepted Answer

Change in the dependent variable for a one-unit increase in that independent variable, holding all other independent variables constant

Answer

Mean of the independent variable

Question 21

Multicollinearity occurs when:

Accepted Answer

Two or more independent variables are highly correlated

Answer

The variance of the error terms is not constant

Answer

The error terms are not normally distributed

Question 22

The purpose of transforming a variable in regression analysis is to:

Accepted Answer

Improve linearity, achieve normality, or stabilize variance

Answer

Reduce the number of variables in the model

Answer

Increase the coefficient of determination

Question 23

The degrees of freedom for the residual sum of squares in an ANOVA table is equal to:

Accepted Answer

Number of observations minus the number of independent variables

Answer

Number of observations

Answer

Number of independent variables

Question 24

The coefficient of determination (R squared) represents the:

Accepted Answer

Proportion of variance in the dependent variable explained by the independent variable

Answer

Significance of the regression model

Answer

Strength of the relationship between the dependent and independent variables

Question 25

The least squares method finds the line that:

Accepted Answer

Minimizes the sum of squared residuals

Answer

Maximizes the coefficient of determination

Answer

Intercepts the y-axis at the origin

Answer

Has the largest slope

Question 26

The slope of the regression line indicates:

Accepted Answer

The change in the dependent variable for a one-unit increase in the independent variable

Answer

The mean of the dependent variable

Answer

The variance of the independent variable

Question 27

The intercept of the regression line represents:

Accepted Answer

The predicted value of the dependent variable when the independent variable is zero

Answer

The mean of the independent variable

Answer

The variance of the dependent variable

Question 28

Which equation represents a simple linear regression model?

Accepted Answer

y = b0 + b1x

Answer

y = (a*x + b)/c

Answer

y = a + b*ln(x)

Answer

y = a*x^2 + b*x + c

Question 29

What is the interpretation of the coefficient of determination (R-squared)?

Accepted Answer

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

Answer

The intercept of the regression line.

Answer

The slope of the regression line.

Question 30

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

Accepted Answer

To visualize the relationship between variables and assess linearity.

Answer

To determine the regression line's parameters.

Answer

To calculate the correlation coefficient.

Question 31

Explain the difference between a positive correlation and a negative correlation.

Accepted Answer

A positive correlation indicates a direct relationship, while a negative correlation indicates an inverse relationship.

Answer

A positive correlation is stronger than a negative correlation.

Question 32

Which statistical measure quantifies the variability of the residuals in a regression model?

Accepted Answer

Standard error of the estimate

Answer

Coefficient of determination

Answer

Intercept of the regression line

Answer

Slope of the regression line

Question 33

What is the primary objective of hypothesis testing in regression analysis?

Accepted Answer

To determine whether there is a statistically significant relationship between variables.

Answer

To estimate the regression model's coefficients.

Answer

To generate predictions for new data points.

Question 34

What is a potential advantage of using a stepwise variable selection method?

Accepted Answer

Reduces model complexity and improves interpretability

Answer

Increases the model's predictive power

Answer

Always identifies the optimal subset of variables

Question 35

Distinguish between a Type I error and a Type II error in regression analysis.

Accepted Answer

A Type I error occurs when the null hypothesis is incorrectly rejected, while a Type II error occurs when the null hypothesis is incorrectly accepted.

Answer

A Type I error is more serious than a Type II error.