Linear regression quiz

Question 1

What is linear regression used for in machine learning?

Accepted Answer

Predicting a continuous numeric value from input features

Answer

Grouping similar data points into clusters

Answer

Classifying emails as spam or not spam

Answer

Reducing the number of features in a dataset

Question 2

Write the equation of a simple linear regression model with one feature.

Accepted Answer

y = mx + b

Answer

y = 1/(1 + e^-x)

Answer

y = mx^2 + b

Answer

y = m/x + b

Question 3

In linear regression, what does the slope coefficient represent?

Accepted Answer

The change in y for a one-unit increase in x

Answer

The value of y when x equals zero

Answer

The total error of the model

Answer

The correlation between two features

Question 4

What does the intercept term (b0) mean in a linear regression model?

Accepted Answer

The predicted y when all features are zero

Answer

The slope of the line

Answer

The average of all y values

Answer

The maximum possible prediction

Question 5

What is the cost function most commonly minimized in linear regression?

Accepted Answer

Mean Squared Error

Answer

Cross-entropy loss

Answer

Hinge loss

Answer

Gini impurity

Question 6

What does the 'least squares' method aim to minimize?

Accepted Answer

The sum of squared residuals

Answer

The sum of the absolute slopes

Answer

The number of data points

Answer

The maximum residual only

Question 7

What is a residual in linear regression?

Accepted Answer

The difference between actual and predicted values

Answer

The slope of the regression line

Answer

The square root of the variance

Answer

The sum of all feature values

Question 8

What is gradient descent and how does it relate to linear regression?

Accepted Answer

An iterative method to minimize the cost function

Answer

A method to plot the regression line

Answer

A way to remove outliers from data

Answer

A technique for splitting train and test sets

Question 9

What role does the learning rate play in gradient descent for linear regression?

Accepted Answer

It controls the step size of each parameter update

Answer

It sets the number of features used

Answer

It determines the slope of the final line

Answer

It measures the accuracy of predictions

Question 10

What is the difference between simple and multiple linear regression?

Accepted Answer

Simple uses one feature, multiple uses several features

Answer

Simple is for classification, multiple for regression

Answer

Simple has no intercept, multiple does

Answer

Simple is nonlinear, multiple is linear

Question 11

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

Accepted Answer

The proportion of variance in the target explained by the model

Answer

The average prediction error in original units

Answer

The number of features in the model

Answer

The slope of the best-fit line

Question 12

If a linear regression model has R-squared = 0, what does that indicate?

Accepted Answer

The model is no better than predicting the mean

Answer

The model fits the data perfectly

Answer

The model has zero error

Answer

The model overfits the data

Question 13

What is the key assumption of linearity in linear regression?

Accepted Answer

The target is a linear combination of the features

Answer

The features must be normally distributed

Answer

The target must be categorical

Answer

The data must have no intercept

Question 14

What is multicollinearity and why is it a problem in linear regression?

Accepted Answer

When features are highly correlated, making coefficients unstable

Answer

When the target has too many categories

Answer

When there are too few data points

Answer

When the learning rate is too high

Question 15

What is overfitting in the context of linear regression?

Accepted Answer

Fitting training noise so the model fails on new data

Answer

Using too few features to capture the pattern

Answer

Having a learning rate that is too small

Answer

Predicting only the mean of the target

Question 16

What is the purpose of L2 regularization (Ridge regression)?

Accepted Answer

It penalizes large squared coefficients to reduce overfitting

Answer

It removes features by setting coefficients exactly to zero

Answer

It increases the learning rate automatically

Answer

It converts regression into classification

Question 17

How does Lasso (L1) regularization differ from Ridge (L2) regularization?

Accepted Answer

Lasso can set coefficients to exactly zero; Ridge only shrinks them

Answer

Lasso uses squared terms; Ridge uses absolute values

Answer

Lasso is for classification; Ridge is for regression

Answer

Lasso always gives higher accuracy than Ridge

Question 18

Why are residuals squared rather than just summed in the cost function?

Accepted Answer

To prevent positive and negative errors from canceling out

Answer

To make the model nonlinear

Answer

To reduce the number of features

Answer

To make all coefficients positive

Question 19

Which scikit-learn class is used to create a basic linear regression model?

Accepted Answer

LinearRegression

Answer

LogisticRegression

Answer

KMeans

Answer

DecisionTreeClassifier

Question 20

After fitting a scikit-learn LinearRegression model, which attributes store the learned slope and intercept?

Accepted Answer

model.coef_ and model.intercept_

Answer

model.slope_ and model.bias_

Answer

model.weights and model.b

Answer

model.params and model.const

Question 21

What is the difference between MAE and MSE as regression error metrics?

Accepted Answer

MSE penalizes large errors more heavily than MAE

Answer

MAE is always larger than MSE

Answer

MAE ignores the sign of errors but MSE does not

Answer

MAE can only be used for classification

Question 22

Why might you scale or standardize features before training a linear regression model with gradient descent?

Accepted Answer

To help gradient descent converge faster and treat features fairly

Answer

To turn the model into a classifier

Answer

To increase the number of features

Answer

To remove the intercept term

Question 23

What does a residual plot showing a clear curved pattern suggest about a linear regression model?

Accepted Answer

The linear model does not capture the true relationship well

Answer

The model is perfectly fitted

Answer

The features are perfectly uncorrelated

Answer

The learning rate is optimal

Question 24

What is the normal equation used for in linear regression?

Accepted Answer

A closed-form formula to directly compute optimal coefficients

Answer

An iterative method like gradient descent

Answer

A way to measure model accuracy

Answer

A method for scaling features

Question 25

How are outliers likely to affect an ordinary least squares regression line?

Accepted Answer

They can strongly pull the line and distort the fit

Answer

They have no effect because errors cancel out

Answer

They always improve the model fit

Answer

They only affect the intercept, never the slope

Question 26

In the linear regression assumption of homoscedasticity, what is required?

Accepted Answer

The residuals have roughly constant variance

Answer

The features are perfectly correlated

Answer

The target is categorical

Answer

The residuals always increase with x

Question 27

What is the relationship between the Pearson correlation coefficient and the slope in simple linear regression?

Accepted Answer

slope = r * (std_y / std_x)

Answer

slope = r squared

Answer

slope = r + intercept

Answer

slope = r / (std_y * std_x)

Question 28

Why might adjusted R-squared be preferred over R-squared when comparing models with different numbers of features?

Accepted Answer

It penalizes adding features that do not improve the model

Answer

It always equals R-squared

Answer

It ignores the number of data points

Answer

It only works for one feature

Question 29

What does it mean if a linear regression model has high bias?

Accepted Answer

The model is too simple and underfits the data

Answer

The model memorizes the training data

Answer

The model has too many features

Answer

The model has zero training error

Question 30

Can linear regression model nonlinear relationships through feature engineering? How?

Accepted Answer

Yes, by adding polynomial or transformed features

Answer

No, it can only ever fit straight lines

Answer

Only by switching to logistic regression

Answer

Only by removing the intercept

Test yourself