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Unit 2: SUPERVISED LEARNING: REGRESSION - Practice Quiz

INT234 — Predictive Analytics 60 Questions
0 Correct 0 Wrong 60 Left
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1 What does simple linear regression model?

Simple Linear Regression Easy
A. The relationship between categories without predictors
B. The relationship between two outcomes
C. The relationship between several outcomes only
D. The relationship between one predictor and one outcome

2 Which equation represents a simple linear regression model?

Simple Linear Regression Easy
A.
B.
C.
D.

3 How many predictor variables are used in multiple linear regression?

Multiple Linear Regression Easy
A. Only one categorical variable
B. Two or more predictor variables
C. One predictor variable
D. No predictor variables

4 Which is an example of multiple linear regression?

Multiple Linear Regression Easy
A. Sorting values from smallest to largest
B. Grouping customers by buying habits
C. Predicting height from weight only
D. Predicting salary from age and experience

5 What type of relationship can polynomial regression model?

Polynomial Regression Easy
A. A curved relationship
B. A relationship with no dependent variable
C. A constant relationship only
D. A categorical relationship only

6 Which term makes a regression model polynomial?

Polynomial Regression Easy
A.
B.
C.
D.

7 What type of outcome is commonly predicted by logistic regression?

Logistic Regression Easy
A. A missing value
B. A continuous measurement only
C. A sorted list
D. A binary outcome

8 What does logistic regression usually estimate before assigning a class?

Logistic Regression Easy
A. A sample mean only
B. A probability
C. A squared error only
D. A correlation table

9 What does ordinary least squares minimize?

Ordinary Least Squares Estimation Easy
A. The number of predictors
B. The largest predictor value
C. The sum of predicted values
D. The sum of squared residuals

10 What is a residual in regression?

Ordinary Least Squares Estimation Easy
A. The number of model variables
B. Predicted value plus actual value
C. Actual value divided by predicted value
D. Actual value minus predicted value

11 What does correlation measure?

Correlations Easy
A. The number of observations in a dataset
B. The average prediction error
C. The strength and direction of a relationship
D. The size of a regression coefficient

12 What does a correlation close to indicate?

Correlations Easy
A. A strong positive relationship
B. No linear relationship
C. A strong negative relationship
D. A perfect prediction error

13 What does Mean Absolute Error measure?

Mean Absolute Error (MAE) Easy
A. The direction of a correlation
B. The proportion of explained variance
C. The average absolute prediction error
D. The average squared predictor value

14 Which formula represents Mean Absolute Error?

Mean Absolute Error (MAE) Easy
A.
B.
C.
D.

15 How are errors treated in Mean Squared Error?

Mean Squared Error (MSE) Easy
A. They are squared before averaging
B. They are converted into percentages
C. They are ranked before averaging
D. They are ignored when negative

16 What happens to large errors in MSE?

Mean Squared Error (MSE) Easy
A. They receive no influence
B. They receive greater influence
C. They are replaced by the median
D. They become negative values

17 What does the R-squared score measure?

R-squared (R²) Score Easy
A. The proportion of outcome variation explained
B. The largest residual in a model
C. The average absolute prediction error
D. The number of predictors in a model

18 What does an R-squared value of usually indicate?

R-squared (R²) Score Easy
A. A model with no predictors
B. The largest possible error
C. A perfect fit to the data
D. No relationship in the data

19 How is RMSE related to MSE?

Root Mean Squared Error (RMSE) Easy
A. RMSE is the square root of MSE
B. RMSE is the sum of MSE values
C. RMSE is the square of MSE
D. RMSE is unrelated to MSE

20 Why is RMSE often easy to interpret?

Root Mean Squared Error (RMSE) Easy
A. It measures only positive correlations
B. It uses the outcome's original units
C. It always equals zero
D. It removes all prediction errors

21 A simple linear regression model is given by . What is the predicted value of when ?

Simple Linear Regression Medium
A.
B.
C.
D.

22 In a simple linear regression model, the slope is . What does this value indicate?

Simple Linear Regression Medium
A. increases by for each unit increase in
B. decreases by for each unit increase in
C. decreases by for each unit increase in
D. remains constant as increases

23 A model predicts house price using , where is the number of rooms and is the number of bathrooms. What is the prediction for a house with 5 rooms and 2 bathrooms?

Multiple Linear Regression Medium
A.
B.
C.
D.

24 In a multiple linear regression model, the coefficient of advertising expenditure is , while holding all other predictors constant. Which interpretation is correct?

Multiple Linear Regression Medium
A. The correlation between advertising and sales is exactly
B. Sales increase by units for each unit increase in advertising
C. Sales increase by units regardless of other predictors
D. Advertising increases by units for each unit increase in sales

25 Which model represents a quadratic polynomial regression model with one predictor?

Polynomial Regression Medium
A.
B.
C.
D.

26 A polynomial regression model fits the training data extremely well but performs poorly on new data. What is the most likely issue?

Polynomial Regression Medium
A. High variance caused by too few features
B. Underfitting caused by excessive bias
C. Perfect generalization caused by a low-degree model
D. Overfitting caused by excessive model complexity

27 A logistic regression model produces a probability of for a positive class. Using a classification threshold of , what class is predicted?

Logistic Regression Medium
A. No class can be assigned
B. Both classes equally
C. The positive class
D. The negative class

28 Why is the sigmoid function used in logistic regression?

Logistic Regression Medium
A. It converts predictions into values between and
B. It forces every predictor to have a positive coefficient
C. It guarantees that the predictors are normally distributed
D. It removes the need for a classification threshold

29 What quantity does ordinary least squares estimation minimize when fitting a regression model?

Ordinary Least Squares Estimation Medium
A. The sum of absolute residuals
B. The correlation between predictors
C. The sum of squared residuals
D. The average of predictor values

30 For a fitted regression line that includes an intercept, what is generally true about the residuals in ordinary least squares estimation?

Ordinary Least Squares Estimation Medium
A. Their absolute values are all equal
B. Their sum is approximately zero
C. Their signs are all positive
D. Their squared values sum to one

31 A correlation coefficient of between two variables indicates which relationship?

Correlations Medium
A. A weak negative linear relationship
B. A strong positive linear relationship
C. No relationship of any type
D. A strong negative linear relationship

32 Two variables have a correlation of . Which conclusion is most appropriate?

Correlations Medium
A. One variable causes the other
B. They have a weak positive linear relationship
C. Their relationship is perfectly nonlinear
D. They have a strong positive relationship

33 A model has actual values and predictions . What is its mean absolute error?

Mean Absolute Error (MAE) Medium
A.
B.
C.
D.

34 Compared with MSE, what is a key characteristic of MAE?

Mean Absolute Error (MAE) Medium
A. MAE is less affected by unusually large errors
B. MAE always produces a value below one
C. MAE can only be used for classification
D. MAE penalizes large errors more heavily

35 A model makes errors of , , and . What is the mean squared error?

Mean Squared Error (MSE) Medium
A.
B.
C.
D.

36 Why can MSE be strongly influenced by a single large prediction error?

Mean Squared Error (MSE) Medium
A. Errors are squared before being averaged
B. Errors are divided by the predictions
C. Errors are converted into percentages
D. Errors are ranked by their signs

37 A regression model has . What is the usual interpretation?

R-squared (R²) Score Medium
A. The predictors explain about of response variance
B. The model's predictions are correct of the time
C. The model makes errors on of observations
D. The correlation between all variables is exactly

38 A model's increases from to after adding a predictor. What does this result show?

R-squared (R²) Score Medium
A. The new predictor definitely causes the response
B. The model's MAE must have increased
C. The model explains more training-set variance
D. The new predictor is statistically significant

39 A model has an MSE of . What is its RMSE?

Root Mean Squared Error (RMSE) Medium
A.
B.
C.
D.

40 Why is RMSE often easier to interpret than MSE for a regression problem?

Root Mean Squared Error (RMSE) Medium
A. RMSE uses the same units as the response
B. RMSE is always smaller than MAE
C. RMSE measures correlation directly
D. RMSE ignores all large errors

41 A simple linear regression is fitted as . The predictor is redefined as , and the model is refitted using the same observations. Which relationship must hold?

Simple Linear Regression Hard
A. The new slope is and the new intercept is
B. The new slope is and the new intercept is
C. The new slope is and the new intercept is
D. The new slope is and the new intercept is

42 For five observations, suppose , , , and . What is the fitted OLS line with an intercept?

Simple Linear Regression Hard
A.
B.
C.
D.

43 The true population model is , with . The population regression of on has slope . If is regressed only on with an intercept, what is the population slope on ?

Multiple Linear Regression Hard
A.
B.
C.
D.

44 A model is written as . Define and . Which coefficients produce the same linear predictor using and ?

Multiple Linear Regression Hard
A.
B.
C.
D.

45 A cubic regression uses the basis . It is refitted in exact arithmetic using and the basis . Assuming full column rank, which statement is correct?

Polynomial Regression Hard
A. Both fitted values and residual sums of squares generally differ
B. Both fitted values and reported coefficients must remain identical
C. The fitted values differ, although the reported coefficients remain identical
D. The fitted values are identical, although the reported coefficients generally differ

46 A quadratic model with columns is fitted to many observations, but every observed is either or . What follows for unregularized OLS?

Polynomial Regression Hard
A. The coefficients are nonunique, but fitted values at observed rows are unique
B. Both the coefficients and fitted values at observed rows are nonunique
C. Both the coefficients and fitted values at observed rows are necessarily unique
D. The coefficients are unique, but fitted values at observed rows are nonunique

47 A logistic model is . Holding fixed, by what factor do the odds change when increases by one unit?

Logistic Regression Hard
A.
B.
C.
D.

48 For , predictions are classified as positive only when . What is the corresponding decision rule for ?

Logistic Regression Hard
A.
B.
C.
D.

49 In an unregularized logistic regression, one predictor perfectly separates all positive observations from all negative observations. What typically happens to maximum-likelihood estimation?

Logistic Regression Hard
A. The likelihood approaches its supremum as some coefficient magnitudes diverge
B. The likelihood remains constant for every possible coefficient vector
C. The likelihood becomes quadratic and yields the ordinary least squares estimate
D. The likelihood reaches a unique maximum with all coefficients equal to zero

50 Assume a full-rank linear model with , but varies across observations. Which statement about OLS is correct?

Ordinary Least Squares Estimation Hard
A. OLS becomes conditionally biased and is necessarily the least efficient linear estimator
B. OLS remains conditionally unbiased, but conventional homoscedastic standard errors can be invalid
C. OLS remains conditionally unbiased and is necessarily the most efficient linear estimator
D. OLS becomes conditionally biased, but conventional homoscedastic standard errors remain valid

51 An OLS model includes an intercept and predictors . Which condition must the fitted residuals satisfy, apart from numerical error?

Ordinary Least Squares Estimation Hard
A. and for every fitted predictor
B. and for every fitted predictor
C. and for every fitted predictor
D. and for every fitted predictor

52 Suppose , , and . What is the partial correlation between and after controlling for ?

Correlations Hard
A. Approximately
B. Approximately
C. Approximately
D. Approximately

53 Variables are transformed as and . If the Pearson correlation between and is , what is the correlation between and ?

Correlations Hard
A.
B.
C.
D.

54 A constant prediction is chosen to minimize empirical MAE for targets . Which set contains all minimizing values of ?

Mean Absolute Error (MAE) Hard
A. Every in
B. Only or
C. Every in
D. Only

55 Model A has residuals , while Model B has residuals . Which comparison is correct?

Mean Absolute Error (MAE) Hard
A. Model A has MAE , while Model B has MAE
B. Model A has MAE , while Model B has MAE
C. Both have MAE , but Model B has the smaller RMSE
D. Both have MAE , but Model A has the smaller RMSE

56 Conditional on a predictor value, with probability and with probability . Which constant prediction minimizes conditional MSE, and what is the minimum MSE?

Mean Squared Error (MSE) Hard
A. Predict , giving minimum MSE
B. Predict , giving minimum MSE
C. Predict , giving minimum MSE
D. Predict , giving minimum MSE

57 A model has MSE on a test subset of observations and MSE on a disjoint subset of observations. What is its MSE on the combined observations?

Mean Squared Error (MSE) Hard
A.
B.
C.
D.

58 On a test set, the total sum of squares around the test-set mean is , while a regression model's residual sum of squares is . What is the test-set ?

R-squared (R²) Score Hard
A.
B.
C.
D.

59 A simple OLS regression with an intercept is fitted on the same sample used to compute a Pearson correlation of between and . What are the model's training and slope sign?

R-squared (R²) Score Hard
A. with a negative slope
B. with a positive slope
C. with a positive slope
D. with a negative slope

60 A model has RMSE on observations and RMSE on another disjoint set of observations. What is the RMSE over all observations?

Root Mean Squared Error (RMSE) Hard
A.
B.
C.
D.
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