Linear Regression

What is the dependent variable in a linear regression model?

• Response variable

• Feature variable

• Independent variable

• Predictor variable

Which method is commonly used to estimate the parameters in a simple linear regression model?

• Gradient descent method

• Maximum likelihood method

• Least squares method

• Bayesian method

What does the coefficient of determination (r²) indicate?

• The slope of the regression line

• The strength of the relationship between variables

• The y-intercept of the regression line

• The total number of observations

In multiple linear regression, what does a high degree of multicollinearity indicate?

• Model has no errors

• Dependent variable is constant

• Independent variables are highly correlated

• Independent variables are uncorrelated

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

• To eliminate multicollinearity

• To reduce the complexity of the model

• To incorporate categorical independent variables

• To increase the number of observations

What does the error term in a linear regression model account for?

• The variability in the independent variable

• The variability in the dependent variable

• The total number of observations

• The slope of the regression line

What is the main goal of the least squares method?

• To maximize the sum of squared errors

• To minimize the sum of squared residuals

• To find the mean of the dependent variable

• To calculate the correlation coefficient

Which of the following is a condition necessary for valid inference in linear regression?

• The error terms must be normally distributed

• The dependent variable must be categorical

• The independent variables must be correlated

• The sample size must be less than 30

What is a potential problem in multiple linear regression if the absolute value of the sample correlation coefficient exceeds 0.7?

• Normality

• Heteroscedasticity

• Autocorrelation

• Multicollinearity

What does the coefficient of determination (R²) indicate in a linear regression model?

• The significance level of the model

• The number of observations in the sample

• The strength of the relationship between independent variables

• The proportion of variability in the dependent variable explained by the model