Master Linear Regression and Classification: A Comprehensive Guide for Machine Learning

Question 1

In linear regression, which hyperparameter controls the balance between bias and variance?

Accepted Answer

Regularization coefficient

Answer

Learning rate

Answer

Epochs

Answer

Activation function

Question 2

Which assumption is NOT necessary for the validity of a linear regression model?

Accepted Answer

Multicollinearity, or high correlation among independent variables

Answer

Linearity in the relationship between variables

Answer

Homoscedasticity, or constant variance of errors

Answer

Independence of errors, or the absence of correlation between errors

Question 3

In logistic regression, the relationship between the predictors and the log odds of the dependent variable is modeled using which function?

Accepted Answer

Sigmoid function

Answer

Linear function

Answer

Gaussian distribution

Answer

Hyperbolic tangent

Question 4

Which fundamental assumption underpins linear regression models?

Accepted Answer

A linear relationship between dependent and independent variables

Answer

Normally distributed observed data

Answer

Uncorrelated independent variables

Answer

Uniformly scattered data points across independent variable range

Question 5

Identify the key assumption of the linear regression model:

Accepted Answer

Linear relationship between variables

Accepted Answer

Normally distributed error terms

Accepted Answer

Constant error variance

Answer

Absence of multicollinearity

Question 6

What is a key assumption of linear regression?

Accepted Answer

The variance of the errors is constant.

Answer

The relationship between the independent and dependent variables is nonlinear.

Answer

The independent variables are not correlated.

Answer

The dependent variable is normally distributed.

Question 7

Which of the following is NOT a fundamental assumption underlying linear regression models?

Accepted Answer

Normally distributed errors

Answer

Linear relationship between variables

Answer

Uncorrelated errors

Answer

Constant variance of errors

Question 8

In linear regression, which assumption is crucial?

Accepted Answer

Linear relationship between variables

Answer

Non-linear relationship between variables

Answer

Unequal spread of residuals

Question 9

In linear regression, what is the primary purpose of the Ordinary Least Squares (OLS) estimation method?

Accepted Answer

Determine the line of best fit for a given dataset

Answer

Predict the intercept of the regression line

Answer

Calculate the variance of the residuals

Answer

Estimate the probability of a data point belonging to a specific class

Question 10

In Logistic Regression, what is the primary reason for using the sigmoid function?

Accepted Answer

To introduce non-linearity, allowing for the prediction of binary outcomes between 0 and 1.

Answer

To minimize the mean squared error, improving model accuracy.

Answer

To stabilize model weights during training, preventing overfitting.

Question 11

Which assumption in linear regression states that the relationship between the dependent and independent variables can be represented by a straight line?

Accepted Answer

Linearity

Answer

Homoscedasticity

Answer

Independence

Answer

Normality

Question 12

Which technique is used to reduce overfitting in linear regression models?

Accepted Answer

L1 regularization

Answer

Data augmentation

Answer

Decision tree pruning

Question 13

In linear regression, what is the assumption about the relationship between the independent and dependent variables?

Accepted Answer

The relationship is inherently linear, even if data points may not align precisely.

Answer

The relationship is perfectly linear, with no errors.

Answer

The relationship is curvilinear, conforming to a parabolic or exponential pattern.

Question 14

In a decision tree, which measure quantifies the level of disorder or uncertainty within a node, aiding in effective node splitting?

Accepted Answer

Entropy

Accepted Answer

Gini Index

Answer

Variance

Answer

Information Gain

Question 15

In linear regression, what is the primary assumption about the relationship between the independent and dependent variables?

Accepted Answer

Linearity

Answer

Normal distribution of errors

Answer

Constant error variance

Answer

Independence of independent variables

Question 16

In linear regression, which feature selection technique quantifies the correlation between each feature and the target variable to determine the most relevant features?

Accepted Answer

Correlation-based Feature Selection

Answer

Forward Selection

Answer

Backward Selection

Answer

Wrapper Feature Selection

Question 17

In logistic regression, which function is primarily used to estimate model parameters by measuring the discrepancy between predicted probabilities and actual class labels?

Accepted Answer

Cross-Entropy Loss

Answer

Mean Squared Error (MSE)

Answer

L1 Regularization

Question 18

In linear regression, which assumption ensures the validity and reliability of the model's predictions by specifying the statistical distribution of the residuals?

Accepted Answer

The residuals follow a normal distribution.

Answer

The residuals are spread evenly across all possible values.

Answer

The residuals follow a Poisson distribution.

Question 19

What mathematical function does logistic regression use to model the probability of an event?

Accepted Answer

Sigmoid function

Answer

Linear function

Answer

Polynomial function

Question 20

In linear regression, which regularization technique is commonly employed to minimize overfitting?

Accepted Answer

L1 Regularization (Lasso)

Accepted Answer

L2 Regularization (Ridge)

Answer

Dropout

Answer

Bagging

Question 21

In supervised machine learning, which technique is primarily used for dimensionality reduction?

Accepted Answer

Principal Component Analysis (PCA)

Answer

Logistic Regression

Answer

Support Vector Machines (SVM)

Answer

Decision Trees

Question 22

In linear regression, what is the primary assumption about the relationship between the independent and dependent variables?

Accepted Answer

The relationship is linear.

Answer

The relationship is perfectly linear.

Answer

The relationship is non-linear.

Answer

The relationship is exponential.

Question 23

In linear regression, we aim to balance model complexity and accuracy through the bias-variance tradeoff. Which action will typically reduce both bias and variance in the resulting model?

Accepted Answer

Increase regularization strength

Answer

Decrease training sample size

Answer

Use a non-linear kernel in SVM

Answer

Add irrelevant features

Question 24

Compared to more complex models like decision trees or support vector machines, a key limitation of logistic regression is that it:

Accepted Answer

Assumes a linear relationship between input features and log odds of the target variable.

Answer

Can only handle binary classification problems.

Answer

Is computationally more expensive than other models.

Answer

Is not prone to overfitting and does not require regularization.

Question 25

In evaluating a linear regression model, which metric measures the model's ability to accurately identify and exclude irrelevant data points?

Accepted Answer

True Negative Rate (TNR)

Answer

Accuracy

Answer

False Negative Rate (FNR)

Answer

Precision

Question 26

In regression modeling, which metric assesses the model's fit to the data?

Accepted Answer

R-squared

Answer

Accuracy

Answer

Precision

Answer

F1-score

Question 27

In ordinary least squares (OLS) estimation, the assumption of exogeneity implies what about the error term and the independent variables in a linear regression model?

Accepted Answer

They are not correlated

Answer

They have constant variance

Answer

They have a linear relationship

Question 28

In logistic regression, the sigmoid function is used to convert the linear combination of features into a probability estimate. What is the primary purpose of using the sigmoid function?

Accepted Answer

To ensure that the predicted probabilities lie between 0 and 1

Answer

To make the model more robust to outliers

Answer

To increase the computational efficiency of the model

Answer

To reduce the overfitting of the model

Question 29

In the context of Support Vector Machines (SVM), what is the primary purpose of the kernel function?

Accepted Answer

To transform non-linearly separable data into a higher-dimensional space, allowing for linear decision boundaries.

Answer

To reduce the data's dimensionality, enhancing computational efficiency.

Answer

To smooth the data and remove noise, improving SVM accuracy.

Answer

To generate random data points to augment the dataset and enhance SVM performance.

Question 30

In linear regression, which assumption is made about the distribution of the residuals?

Accepted Answer

Normal distribution

Answer

Uniform distribution

Answer

Exponential distribution

Answer

Binomial distribution

Question 31

In linear regression, which assumption ensures that the error terms associated with different observations are statistically independent of each other?

Accepted Answer

Independence

Answer

Homoscedasticity

Answer

Normality

Answer

Linearity

Question 32

In logistic regression, which assumption describes the relationship between the independent variables and the dependent variable?

Accepted Answer

The logit of the probability of the dependent variable being 1 is a linear function of the independent variables

Answer

Linear relationship

Answer

Normal distribution of the independent variables

Answer

Homoscedasticity of the residuals

Question 33

In linear regression, what is the assumed relationship between the independent and dependent variables?

Accepted Answer

Linear

Answer

Non-linear

Answer

Exponential

Answer

Logarithmic

Question 34

Which regularization technique promotes sparsity in linear regression models by penalizing the sum of the absolute values of coefficients?

Accepted Answer

L1 regularization

Answer

L2 regularization

Answer

Dropout

Question 35

When evaluating a linear regression model's performance in predicting continuous target variables, which metric is commonly used?

Accepted Answer

Root Mean Squared Error (RMSE)

Answer

Accuracy

Answer

Precision

Answer

F1-score

Question 36

In linear regression, which assumption is made about the variance of the error term?

Accepted Answer

The variance of the error term is constant for all values of the independent variables.

Answer

The variance of the error term increases as the value of the independent variable increases.

Answer

The variance of the error term is inversely proportional to the value of the independent variable.

Answer

The variance of the error term is randomly distributed and independent of the independent variables.

Question 37

Which of the following metrics is not specifically used for evaluating linear regression models?

Accepted Answer

Accuracy

Answer

Mean absolute error (MAE)

Answer

Root mean squared error (RMSE)

Answer

R-squared

Question 38

What is the mathematical equation that defines a linear regression line?

Accepted Answer

y = mx + b

Answer

y = mx^2 + b

Answer

y = e^(mx + b)

Answer

y = ln(mx + b)

Question 39

In which real-world scenario is linear regression commonly employed?

Accepted Answer

Predicting the selling price of a house based on its features

Answer

Detecting fraudulent transactions based on financial data

Answer

Classifying images of animals based on their visual characteristics

Answer

Generating natural language text for a chatbot

Question 40

In a linear regression model, what does the coefficient associated with a feature represent?

Accepted Answer

The average change in the target variable for a one-unit increase in the feature, assuming other features remain constant

Answer

The probability of the target variable taking a specific value given the feature

Answer

The relative importance of the feature compared to other features

Answer

The error in predicting the target variable using the feature

Question 41

Which of the following is NOT a commonly used evaluation metric for classification models?

Accepted Answer

Root Mean Squared Error (RMSE)

Answer

Accuracy

Answer

F1 Score

Question 42

Which technique is NOT used for regularization in linear regression models?

Accepted Answer

Dropout

Answer

L1 regularization

Answer

L2 regularization

Answer

Elastic net regularization

Question 43

In logistic regression, what distinctive characteristic does the sigmoid function possess?

Accepted Answer

Produces continuous output values between 0 and 1

Answer

Linear function passing through the origin

Answer

Step function taking only 0 and 1 as output

Answer

Transforms input features into a linear combination

Question 44

Which assumption is NOT required for linear regression?

Accepted Answer

Independent variables are correlated (multicollinearity)

Answer

Linear relationship between the dependent and independent variables

Answer

Constant variance of error terms (homoscedasticity)

Answer

Normally distributed residuals

Question 45

In logistic regression, what is the primary assumption regarding the dependent variable?

Accepted Answer

Binary nature (0 or 1)

Answer

Linear relationship with the independent variables

Answer

Mutual independence of independent variables

Answer

Normal distribution of the error term

Question 46

Which of the following is NOT a measure of model performance in linear regression?

Accepted Answer

Accuracy

Answer

Mean absolute error (MAE)

Answer

Root mean squared error (RMSE)

Answer

R-squared

Question 47

In linear regression, the coefficient of determination (R-squared) indicates:

Accepted Answer

The proportion of variance in the response variable explained by the model

Answer

The squared correlation between the predicted and actual values

Answer

The mean error of the model

Answer

The number of independent variables in the model

Question 48

Regularization techniques are used in linear regression to:

Accepted Answer

Reduce overfitting and improve model generalization

Answer

Increase the number of features in the model

Answer

Automate the feature selection process

Answer

Speed up the training time of the model

Question 49

In linear classification, the sigmoid function is commonly used as the:

Accepted Answer

Activation function

Answer

Loss function

Answer

Regularization term

Answer

Normalization function

Question 50

Regularization in logistic regression can help to:

Accepted Answer

Prevent overfitting and improve model accuracy

Answer

Reduce the number of features in the model

Answer

Increase the training time of the model

Answer

Speed up the inference time of the model

Question 51

Which of the following is a typical application of linear classification?

Accepted Answer

Spam detection

Answer

Image recognition

Answer

Time series forecasting

Answer

Financial market prediction

Question 52

The cost function in linear regression is typically:

Accepted Answer

Mean squared error (MSE)

Answer

Cross-entropy loss

Answer

Hinge loss

Answer

Negative log likelihood

Question 53

Linear discriminant analysis (LDA) aims to:

Accepted Answer

Find a linear combination of features that best discriminates between different classes

Answer

Maximize the variance within classes

Answer

Minimize the variance between classes

Answer

Normalize the feature values

Question 54

In logistic regression, what is the primary assumption about the dependent variable?

Accepted Answer

It is binary.

Answer

It is continuous.

Answer

It is normally distributed.

Question 55

In binary linear classification, what is the main purpose of a threshold value?

Accepted Answer

To categorize data points into classes based on their predicted probabilities

Answer

To modify the slope of the classification line

Answer

To address missing values in the dataset

Answer

To decrease the data's dimensionality

Question 56

In logistic regression, the sigmoid function is primarily used as the activation function because it:

Accepted Answer

Is non-linear and can model complex relationships between features and the outcome.

Answer

Is a linear function that maps inputs to binary values.

Answer

Assists in optimizing model coefficients using gradient descent.

Answer

Is computationally efficient and allows for faster model training.

Question 57

Which regularization technique in linear regression penalizes the sum of squared coefficients?

Accepted Answer

Ridge regression

Answer

Lasso regression

Answer

Elastic net regression

Answer

Cross-validation

Question 58

In logistic regression, the sigmoid activation function generates an output. What does this output mathematically represent?

Accepted Answer

Probability of the input belonging to the positive class

Answer

Estimated value of the target variable

Answer

Log odds of the input belonging to the positive class

Question 59

For a dataset exhibiting a non-linear relationship between its dependent and independent variables, which regression technique is most appropriate?

Accepted Answer

Polynomial regression

Answer

Simple linear regression

Answer

Multiple linear regression

Answer

Logistic regression

Question 60

Which regularization technique penalizes model coefficients for deviations from zero, leading to a sparser model?

Accepted Answer

L1 regularization (Lasso)

Answer

L2 regularization (Ridge)

Answer

Elastic net regularization

Answer

Ridge regression

Question 61

In logistic regression, the sigmoid function is used to:

Accepted Answer

Transform odds into probabilities

Answer

Transform probabilities into odds

Answer

Linearize the relationship between the independent and dependent variables

Answer

Regularize the model coefficients

Question 62

The accuracy of a classification model is commonly measured using which metric?

Accepted Answer

F1 score

Answer

Mean absolute error

Answer

Root mean squared error

Answer

R-squared

Question 63

A potential limitation of linear regression is its inability to:

Accepted Answer

Handle nonlinear relationships

Answer

Be sensitive to outliers

Answer

Assume a normal distribution of errors

Answer

Require a large sample size

Question 64

In binary classification, a receiver operating characteristic (ROC) curve plots:

Accepted Answer

True positive rate (sensitivity) vs. false positive rate (1 - specificity)

Answer

Precision vs. recall

Answer

F1 score vs. accuracy

Answer

Loss vs. number of iterations