1What is the primary goal of Simple Linear Regression?
A.To group similar data points together
B.To reduce the dimensionality of the dataset
C.To classify data into discrete categories
D.To find the relationship between two continuous variables using a straight line
Correct Answer: To find the relationship between two continuous variables using a straight line
Explanation:
Simple Linear Regression aims to model the relationship between a single independent variable and a dependent variable by fitting a linear equation to observed data.
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2In the linear regression equation Y = mx + c, what does 'c' represent?
A.The y-intercept
B.The dependent variable
C.The slope of the line
D.The error term
Correct Answer: The y-intercept
Explanation:
In the equation Y = mx + c, 'c' is the y-intercept, which represents the value of Y when x is 0.
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3Which method is commonly used to estimate the coefficients in linear regression?
A.Ordinary Least Squares (OLS)
B.Principal Component Analysis
C.Maximum Likelihood Estimation
D.K-Means Clustering
Correct Answer: Ordinary Least Squares (OLS)
Explanation:
Ordinary Least Squares (OLS) is the most common method used to estimate the parameters of a linear regression model by minimizing the sum of the squares of the differences between observed and predicted values.
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4What is a 'residual' in the context of regression?
A.The value of the independent variable
B.The difference between the observed value and the predicted value
C.The slope of the regression line
D.The square of the correlation coefficient
Correct Answer: The difference between the observed value and the predicted value
Explanation:
A residual is the vertical distance between a data point and the regression line, calculated as (Actual Value - Predicted Value).
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5Which of the following values indicates a perfect negative correlation?
A.0
B.-1
C.0.5
D.1
Correct Answer: -1
Explanation:
A Pearson correlation coefficient of -1 indicates a perfect negative linear relationship between two variables.
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6Multiple Linear Regression differs from Simple Linear Regression because it involves:
A.Polynomial terms
B.Multiple dependent variables
C.Multiple independent variables
D.Categorical outputs
Correct Answer: Multiple independent variables
Explanation:
Multiple Linear Regression models the relationship between two or more independent variables (features) and a single dependent variable.
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7In a regression model, if the R-squared value is 0.85, what does this mean?
A.85% of the errors are zero
B.85% of the variance in the dependent variable is explained by the independent variables
C.The correlation coefficient is 0.85
D.The model is 85% accurate in classification
Correct Answer: 85% of the variance in the dependent variable is explained by the independent variables
Explanation:
R-squared represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model.
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8Which evaluation metric is calculated by taking the average of the squared differences between predicted and actual values?
A.R-squared
B.MSE
C.MAE
D.RMSE
Correct Answer: MSE
Explanation:
Mean Squared Error (MSE) measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the actual value.
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9Which regression algorithm is specifically designed to predict the probability of a categorical outcome (e.g., Yes/No)?
A.Polynomial Regression
B.Simple Linear Regression
C.Ridge Regression
D.Logistic Regression
Correct Answer: Logistic Regression
Explanation:
Logistic Regression is used for binary classification problems to predict the probability of an instance belonging to a specific class.
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10What function is used in Logistic Regression to map predicted values to probabilities between 0 and 1?
A.Polynomial function
B.ReLU function
C.Linear function
D.Sigmoid (Logistic) function
Correct Answer: Sigmoid (Logistic) function
Explanation:
The Sigmoid function maps any real-valued number into a value between 0 and 1, making it suitable for probability estimation in Logistic Regression.
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11Polynomial Regression is best used when:
A.The relationship between variables is non-linear
B.The dependent variable is categorical
C.There are too many independent variables
D.The relationship between variables is linear
Correct Answer: The relationship between variables is non-linear
Explanation:
Polynomial Regression models a non-linear relationship between the independent and dependent variables by adding powers of the independent variable.
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12What is a potential risk of using a high-degree polynomial in Polynomial Regression?
A.High bias
B.Overfitting
C.Linearity
D.Underfitting
Correct Answer: Overfitting
Explanation:
Using a high-degree polynomial allows the model to fit the training data very closely, often capturing noise and fluctuations, leading to overfitting and poor generalization to new data.
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13Root Mean Squared Error (RMSE) is preferred over MSE when:
A.You want to penalize outliers less
B.You want a value between 0 and 1
C.You have a classification problem
D.You want the error metric to be in the same units as the target variable
Correct Answer: You want the error metric to be in the same units as the target variable
Explanation:
RMSE is the square root of MSE, which brings the error metric back to the original units of the target variable, making it more interpretable.
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14Which metric is less sensitive to outliers?
A.RMSE
B.MAE
C.R-squared
D.MSE
Correct Answer: MAE
Explanation:
Mean Absolute Error (MAE) takes the absolute difference without squaring, meaning large errors (outliers) do not contribute disproportionately to the total error compared to MSE or RMSE.
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15In OLS estimation, the assumption of 'Homoscedasticity' implies that:
A.The residuals follow a normal distribution
B.The residuals have constant variance across all levels of the independent variable
C.The relationship is non-linear
D.There is no correlation between independent variables
Correct Answer: The residuals have constant variance across all levels of the independent variable
Explanation:
Homoscedasticity means that the spread (variance) of the residuals is consistent for all predicted values. If the spread changes (e.g., cone shape), it is Heteroscedasticity.
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16Multicollinearity in Multiple Linear Regression refers to:
A.A high correlation between two or more independent variables
B.A high correlation between the dependent and independent variables
C.The lack of a linear relationship
D.Measurement errors in the target variable
Correct Answer: A high correlation between two or more independent variables
Explanation:
Multicollinearity occurs when independent variables in a regression model are highly correlated with each other, making it difficult to isolate the individual effect of each variable.
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17The range of the R-squared (R²) score is typically:
A.-1 to 1
B.0 to 1
C.-infinity to 1
D.0 to infinity
Correct Answer: 0 to 1
Explanation:
R-squared typically ranges from 0 to 1, where 1 indicates a perfect fit. However, it can be negative for arbitrarily poor models that perform worse than a horizontal mean line.
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18In the equation Y = b0 + b1x1 + b2x2 + ... + bn*xn, what are b1, b2, ... bn called?
A.Dependent variables
B.Residuals
C.Regression coefficients
D.Intercepts
Correct Answer: Regression coefficients
Explanation:
These are the regression coefficients (or weights) that represent the change in the dependent variable for a one-unit change in the respective independent variable.
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19Which of the following is NOT an assumption of Linear Regression?
A.Multicollinearity usually present
B.Independence of errors
C.Linearity
D.Normality of residuals
Correct Answer: Multicollinearity usually present
Explanation:
Linear Regression assumes little to no multicollinearity. The presence of significant multicollinearity is a violation of assumptions.
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20What is the primary advantage of Adjusted R-squared over R-squared?
A.It can handle non-linear data
B.It penalizes the addition of irrelevant independent variables
C.It is always higher than R-squared
D.It is easier to calculate
Correct Answer: It penalizes the addition of irrelevant independent variables
Explanation:
Regular R-squared never decreases when new variables are added, even if they are useless. Adjusted R-squared accounts for the number of predictors and decreases if a new term improves the model less than expected by chance.
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21In Logistic Regression, the 'Logit' is defined as:
A.The sum of squared errors
B.The square root of the variance
C.The natural logarithm of the odds ratio
D.The probability of success
Correct Answer: The natural logarithm of the odds ratio
Explanation:
The Logit function is the log-odds, defined as log(p / (1-p)), which transforms the probability to a value ranging from negative to positive infinity, suitable for linear modeling.
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22If the Pearson correlation coefficient between X and Y is 0, it implies:
A.There is no linear relationship between X and Y
B.There is a strong non-linear relationship
C.X causes Y
D.X and Y are identical
Correct Answer: There is no linear relationship between X and Y
Explanation:
A correlation of 0 indicates no linear relationship, though a non-linear relationship could still exist.
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23Which cost function is primarily used for Logistic Regression?
A.Log Loss (Cross-Entropy)
B.Hinge Loss
C.Mean Squared Error
D.Mean Absolute Error
Correct Answer: Log Loss (Cross-Entropy)
Explanation:
Log Loss (or Binary Cross-Entropy) is the standard cost function for Logistic Regression because using MSE would result in a non-convex function that is hard to optimize.
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24When evaluating a regression model, a lower MAE indicates:
A.Better performance
B.Overfitting
C.Worse performance
D.High variance
Correct Answer: Better performance
Explanation:
MAE measures the average magnitude of errors. A value closer to 0 indicates the predictions are closer to the actual values.
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25To handle categorical independent variables in regression, one should usually:
A.Use the text directly
B.Convert them using One-Hot Encoding (Dummy variables)
C.Assign random numbers
D.Ignore them
Correct Answer: Convert them using One-Hot Encoding (Dummy variables)
Explanation:
Regression models require numerical input. Categorical variables are converted into dummy variables (0s and 1s) to be processed.
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26The 'Dummy Variable Trap' occurs when:
A.Categorical variables are missing
B.One dummy variable can be predicted perfectly from the others (perfect multicollinearity)
C.The variables are not scaled
D.There are too many categories
Correct Answer: One dummy variable can be predicted perfectly from the others (perfect multicollinearity)
Explanation:
This happens if you include a dummy variable for every category. The sum of all dummy variables equals 1 (the intercept term), causing perfect multicollinearity. One category should be dropped to avoid this.
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27Which of the following plots is best for visualizing a Simple Linear Regression?
A.Pie Chart
B.Scatter Plot with a line of best fit
C.Histogram
D.Box Plot
Correct Answer: Scatter Plot with a line of best fit
Explanation:
A scatter plot displays the relationship between two continuous variables, and the line of best fit visualizes the regression model.
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28If a polynomial regression model has degree 1, it behaves like:
A.An Exponential Regression
B.A Simple Linear Regression
C.A Quadratic Regression
D.A Logistic Regression
Correct Answer: A Simple Linear Regression
Explanation:
A polynomial of degree 1 is simply y = b0 + b1*x, which is the equation for a straight line (Simple Linear Regression).
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29In the context of MSE, what is the effect of squaring the errors?
A.It reduces the impact of outliers
B.It cancels out positive and negative errors
C.It makes the calculation faster
D.It penalizes larger errors more severely than smaller errors
Correct Answer: It penalizes larger errors more severely than smaller errors
Explanation:
Squaring the difference ensures that all errors are positive and that larger errors contribute disproportionately more to the total score, forcing the model to minimize large deviations.
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30Which algorithm minimizes the sum of squared residuals?
A.Logistic Regression
B.Ordinary Least Squares
C.Gradient Boosting
D.Decision Trees
Correct Answer: Ordinary Least Squares
Explanation:
The fundamental mathematical principle behind standard linear regression is OLS, which explicitly minimizes the sum of squared residuals.
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31What is the typical threshold used in Logistic Regression to classify a probability as '1' (or Positive)?
A.0.1
B.0.5
C.1.0
D.0.0
Correct Answer: 0.5
Explanation:
While adjustable, the standard default threshold is 0.5. Probabilities >= 0.5 are classified as positive (1), and < 0.5 as negative (0).
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32Predicting the price of a house based on size, location, and age is a problem of:
A.Dimensionality Reduction
B.Clustering
C.Regression
D.Classification
Correct Answer: Regression
Explanation:
Predicting a continuous numerical value (price) is a Regression task.
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33Predicting whether an email is 'Spam' or 'Not Spam' is a problem of:
Predicting a categorical outcome (binary in this case) is a classification task, for which Logistic Regression is suitable.
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34In the equation Y = b0 + b1*X + e, what does 'e' represent?
A.The correlation
B.The error term (noise)
C.The intercept
D.The predicted value
Correct Answer: The error term (noise)
Explanation:
The term 'e' (epsilon) represents the error term, accounting for the variance in Y that is not explained by the linear relationship with X.
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35If the correlation coefficient (r) is 0.9, the Coefficient of Determination (R²) is:
A.0.81
B.0.18
C.0.9
D.0.45
Correct Answer: 0.81
Explanation:
In simple linear regression, R-squared is the square of the Pearson correlation coefficient ().
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36Which of the following indicates the strongest relationship?
A.Correlation = 0.7
B.Correlation = 0.5
C.Correlation = 0.1
D.Correlation = -0.8
Correct Answer: Correlation = -0.8
Explanation:
The strength of a relationship is determined by the absolute value of the correlation. |-0.8| = 0.8, which is higher than 0.7 or 0.5.
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37Why might one perform a log transformation on the dependent variable in regression?
A.To reduce the sample size
B.To turn it into a categorical variable
C.To make the distribution more normal or linearize a relationship
D.To increase the number of outliers
Correct Answer: To make the distribution more normal or linearize a relationship
Explanation:
Log transformations are often used to handle skewed data or to transform a non-linear exponential relationship into a linear one.
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38If a model has an RMSE of 10 and an MAE of 2, what does this suggest?
A.The model is underfitting
B.The model is perfect
C.RMSE is calculated incorrectly
D.There are likely large outliers in the errors
Correct Answer: There are likely large outliers in the errors
Explanation:
Because RMSE squares errors, it is much more sensitive to outliers than MAE. A large gap between MAE and RMSE suggests the presence of large error values (outliers).
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39In polynomial regression, if the curve passes through every single data point perfectly, the model is likely:
A.Underfitted
B.Ideally fitted
C.Linear
D.Overfitted
Correct Answer: Overfitted
Explanation:
Fitting every point perfectly usually means the model has captured the noise rather than the underlying pattern, leading to overfitting.
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40The decision boundary in Logistic Regression is:
A.Undefined
B.Circular
C.Linear (in the feature space)
D.Curved
Correct Answer: Linear (in the feature space)
Explanation:
Standard Logistic Regression creates a linear decision boundary that separates the classes in the feature space.
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41What is the slope of the line y = 3x + 5?
A.5
B.3
C.0
D.8
Correct Answer: 3
Explanation:
In the slope-intercept form , is the slope. Here, .
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42When comparing two regression models on the same dataset, the one with the ___ is generally preferred.
A.Higher MAE
B.Higher R-squared and Lower RMSE
C.Lower R-squared
D.Higher RMSE
Correct Answer: Higher R-squared and Lower RMSE
Explanation:
A better model explains more variance (higher R²) and has smaller average errors (lower RMSE).
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43Which technique helps checks for 'Linearity' in a regression model?
A.Histogram of the target
B.Bar chart
C.Residuals vs Predicted Values plot
D.Correlation matrix
Correct Answer: Residuals vs Predicted Values plot
Explanation:
A plot of residuals versus predicted values should show a random scatter. If there is a pattern (like a curve), the linearity assumption is violated.
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44The 'Bias-Variance Tradeoff' implies that:
A.As we increase model complexity, bias decreases but variance increases
B.Complex models have high bias
C.Simple models have high variance
D.We want high bias and high variance
Correct Answer: As we increase model complexity, bias decreases but variance increases
Explanation:
Simple models (high bias) miss patterns. Complex models (high variance) overfit. The goal is to find the sweet spot.
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45Feature scaling (normalization/standardization) is particularly important for:
A.Decision Trees
B.Ordinary Least Squares solution
C.Simple Linear Regression with one variable
D.Regression using Gradient Descent optimization
Correct Answer: Regression using Gradient Descent optimization
Explanation:
While OLS is scale-invariant analytically, optimization algorithms like Gradient Descent converge much faster when features are on a similar scale.
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46If R-squared is 1.0:
A.The model predicts the mean for every observation
B.The model explains 100% of the variability in the data
C.The correlation is 0
D.The model is completely wrong
Correct Answer: The model explains 100% of the variability in the data
Explanation:
An R-squared of 1.0 means the model perfectly fits the data, and the regression line passes through all observed points.
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47Which of the following is a dependent variable in a study of how study time affects exam scores?
A.Student ID
B.Study time
C.Subject
D.Exam scores
Correct Answer: Exam scores
Explanation:
The dependent variable is the outcome we are trying to predict. Here, exam scores depend on the study time.
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48In the context of regression, 'extrapolation' refers to:
A.Predicting values outside the range of the training data
B.Calculating the mean
C.Removing outliers
D.Predicting values within the range of training data
Correct Answer: Predicting values outside the range of the training data
Explanation:
Extrapolation involves making predictions for independent variable values that are outside the range of data used to train the model, which is risky.
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49The correlation coefficient ranges between:
A.0 and 1
B.-1 and 1
C.-infinity and infinity
D.0 and 100
Correct Answer: -1 and 1
Explanation:
Pearson's correlation coefficient is always between -1 (perfect negative) and +1 (perfect positive).
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50Which of the following is NOT a metric for Regression?
A.MSE
B.Accuracy
C.R-squared
D.MAE
Correct Answer: Accuracy
Explanation:
Accuracy is a classification metric (percentage of correct classes). It does not apply to regression, where errors are continuous values.