Top 10 Multiple Choice Quiz Questions on Linear Regression with Answers (Concept-Based MCQs)
Are you learning Linear Regression and want to test your understanding? Here are 10 carefully selected concept-based multiple-choice questions (MCQs) on Linear Regression — covering assumptions, coefficients, R², and model behavior. Each question includes an explanation to strengthen your understanding of this core machine learning concept.
1. The main objective of linear regression is to:
A. Minimize classification error
B. Maximize correlation between X and Y
C. Minimize the sum of squared residuals
D. Maximize the slope coefficient
Answer: C
Explanation: Linear regression finds the line that minimizes the residual sum of squares (RSS) between predicted and actual values.
2. If the correlation coefficient (r) between X and Y is 0, what does linear regression conclude?
A. The slope is zero
B. The intercept is zero
C. Y perfectly predicts X
D. The model fits well
Answer: A
Explanation: Zero correlation implies no linear relationship — hence the slope (β₁) will be approximately zero.
3. In the linear model Ŷ = β₀ + β₁X, β₀ represents:
A. The rate of change in Y
B. The average of Y
C. The predicted Y when X = 0
D. The correlation between X and Y
Answer: C
Explanation: The intercept (β₀) is the predicted value of Y when X = 0.
4. Which of the following assumptions is not required for linear regression?
A. Linearity between X and Y
B. Independence of errors
C. Homoscedasticity of errors
D. X and Y must both be normally distributed
Answer: D
Explanation: Only residuals (errors) need to be approximately normal — not X or Y individually.
5. Which metric is commonly used to measure how well a linear regression model fits the data?
A. Precision
B. Recall
C. R² (Coefficient of Determination)
D. F1-score
Answer: C
Explanation: R² shows the proportion of variance in Y explained by X — a key measure of fit.
6. Multicollinearity occurs when:
A. The dependent variable is categorical
B. Independent variables are highly correlated with each other
C. Errors are not normally distributed
D. There are too few samples
Answer: B
Explanation: High correlation among predictors (X’s) makes it difficult to isolate individual effects.
7. What will happen if outliers are present in the dataset used for linear regression?
A. The model will ignore them
B. The slope and intercept may get distorted
C. R² value will always increase
D. Predictions will be unaffected
Answer: B
Explanation: Linear regression is sensitive to outliers, which can heavily influence the line of best fit.
8. Which of the following best describes “overfitting” in regression?
A. Model fits training data too well but performs poorly on new data
B. Model has high bias and low variance
C. Model ignores noise in data
D. Model underestimates relationships
Answer: A
Explanation: Overfitting captures noise instead of the true relationship, reducing generalization.
9. In multiple regression, the adjusted R² is preferred over R² because:
A. It always increases with more predictors
B. It penalizes adding irrelevant predictors
C. It is easier to compute
D. It does not depend on sample size
Answer: B
Explanation: Adjusted R² adjusts for the number of predictors, preventing artificial inflation of fit quality.
10. Gradient descent is used in regression to:
A. Compute the correlation coefficient
B. Find optimal β₀ and β₁ by minimizing the cost function
C. Calculate residuals
D. Scale input features
Answer: B
Explanation: Gradient descent iteratively updates coefficients to minimize the cost function (mean squared error).
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