Linear Regression Quiz

What is the primary objective of linear regression?

• Minimize the sum of squared errors

• Maximize the correlation coefficient

• Minimize the number of variables

• Maximize the residual sum of squares

In simple linear regression, the relationship between the independent variable (X) and the dependent variable (Y) is assumed to be:

• Non-linear

• Exponential

• Linear

• Logarithmic

Which of the following is the equation for a simple linear regression model?

• Y=aX^2+bX+c

• Y=b0+b1X+ϵ

• Y=log(X)+c

• Y=e(aX+b)

What does the coefficient b1 represent in the simple linear regression equation?

• The y-intercept

• The slope of the regression line

• The residual error

• The mean of X

What is the method commonly used to estimate the parameters of a linear regression model?

• Maximum Likelihood Estimation (MLE)

• Gradient Descent

• Ordinary Least Squares (OLS)

• K-Nearest Neighbors (KNN)

If the correlation coefficient between X and Y is zero, what does it imply?

• There is no linear relationship between X and Y

• X and Y are independent

• X and Y have a strong nonlinear relationship

• X causes changes in Y

What assumption does linear regression make about the residuals (errors)?

• They must be positively skewed

• They must follow a uniform distribution

• They must be normally distributed with a mean of zero

• They must be proportional to X

Which of the following is a measure of how well the regression line fits the data?

• Mean Squared Error (MSE)

• R-squared (R2)

• p-value

• Variance Inflation Factor (VIF)

What problem can occur if independent variables in multiple linear regression are highly correlated?

• Overfitting

• Heteroscedasticity

• Multicollinearity

• Homoscedasticity

What happens when we add irrelevant features to a linear regression model?

• The model always improves

• The model might overfit and lose interpretability

• The coefficients remain unchanged

• The p-values of all variables decrease