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50 Regression Analysis in Data Analysis MCQs

Category: AI & Data Science MCQDate: Published: November 8, 2025Posted by: MCQs Generator

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These 50 MCQs covers fundamental concepts in regression analysis, including linear and multiple regression, assumptions, diagnostics, and interpretation. Ideal for students and professionals in data analysis to test understanding of predictive modeling techniques.

1. What does linear regression model the relationship between?

a) Two categorical variables

b) A dependent variable and one or more independent variables

c) Only independent variables

d) Time series only

Correct Answer: b) A dependent variable and one or more independent variables

Explanation:

Linear regression predicts a continuous outcome (Y) as a linear function of predictors (X).

2. The slope coefficient in simple linear regression represents

a) The intercept

b) Change in Y for a one-unit change in X

c) The correlation

d) The error term

Correct Answer: b) Change in Y for a one-unit change in X

Explanation:

β1 = ΔY / ΔX, holding other factors constant.

3. R-squared measures

a) Total variance

b) Proportion of variance in Y explained by X

c) Residual sum of squares

d) Standard error

Correct Answer: b) Proportion of variance in Y explained by X

Explanation:

Ranges from 0 to 1; higher values indicate better fit.

4. The assumption of linearity in regression means

a) Constant variance

b) Relationship between X and Y is linear

c) No multicollinearity

d) Independent errors

Correct Answer: b) Relationship between X and Y is linear

Explanation:

Verified via scatter plots or residual plots.

5. Homoscedasticity refers to

a) Constant variance of residuals

b) Normal distribution of errors

c) No autocorrelation

d) Linear trend

Correct Answer: a) Constant variance of residuals

Explanation:

Tested with Breusch-Pagan; violations suggest heteroscedasticity.

6. In multiple regression, multicollinearity is detected using

a) VIF (Variance Inflation Factor)

b) R-squared

c) F-test

d) t-test

Correct Answer: a) VIF (Variance Inflation Factor)

Explanation:

VIF > 5-10 indicates high collinearity among predictors.

7. The intercept in regression is

a) Expected Y when all X=0

b) Slope

c) Error

d) Correlation

Correct Answer: a) Expected Y when all X=0

Explanation:

β0; may lack interpretation if X=0 is outside range.

8. Residuals are

a) Predicted values

b) Observed minus predicted values

c) Independent variables

d) Coefficients

Correct Answer: b) Observed minus predicted values

Explanation:

Used for diagnostics; should be randomly distributed.

9. The F-test in regression tests

a) Overall model significance

b) Individual coefficients

c) Linearity

d) Normality

Correct Answer: a) Overall model significance

Explanation:

H0: all β=0; low p-value indicates model explains variance.

10. t-test for coefficients tests

a) H0: β=0

b) H0: R²=0

c) Intercept only

d) Variance equality

Correct Answer: a) H0: β=0

Explanation:

Significance of individual predictors.

11. Adjusted R-squared accounts for

a) Number of predictors

b) Sample size

c) Both a and b

d) Residuals

Correct Answer: c) Both a and b

Explanation:

Penalizes adding irrelevant variables; better for model comparison.

12. Outliers in regression can be detected using

a) Leverage and Cook's distance

b) R-squared

c) Slope

d) Intercept

Correct Answer: a) Leverage and Cook's distance

Explanation:

High values indicate influential points affecting fit.

13. The standard error of the estimate is

a) Root mean squared error

b) Average residual

c) Variance of Y

d) Correlation

Correct Answer: a) Root mean squared error

Explanation:

Measures prediction accuracy; √(SSE/(n-k-1)).

14. Autocorrelation in residuals is tested with

a) Durbin-Watson test

b) Breusch-Pagan

c) Shapiro-Wilk

d) VIF

Correct Answer: a) Durbin-Watson test

Explanation:

Values near 2 indicate no serial correlation; common in time series.

15. Logistic regression is used for

a) Continuous outcomes

b) Binary or categorical outcomes

c) Time series

d) Clustering

Correct Answer: b) Binary or categorical outcomes

Explanation:

Models log-odds; uses sigmoid function.

16. In ridge regression, the penalty is on

a) Sum of squared coefficients

b) Absolute coefficients

c) Interactions

d) Residuals

Correct Answer: a) Sum of squared coefficients

Explanation:

L2 regularization; reduces multicollinearity.

17. Lasso regression uses

a) L1 penalty

b) L2 penalty

c) No penalty

d) Quadratic penalty

Correct Answer: a) L1 penalty

Explanation:

Sum of absolute coefficients; performs variable selection.

18. Polynomial regression extends linear by

a) Adding higher powers of X

b) Multiple X variables

c) Interactions

d) Log transformation

Correct Answer: a) Adding higher powers of X

Explanation:

Captures non-linear relationships; risks overfitting.

19. The coefficient of determination is

a) R-squared

b) Correlation coefficient

c) Standard error

d) F-statistic

Correct Answer: a) R-squared

Explanation:

1 - (SS_res / SS_tot).

20. Normality of residuals is tested with

a) Q-Q plot or Shapiro-Wilk

b) Scatter plot

c) Histogram of X

d) VIF plot

Correct Answer: a) Q-Q plot or Shapiro-Wilk

Explanation:

Assumption for inference; affects confidence intervals.

21. In OLS regression, the goal is to minimize

a) Sum of squared residuals

b) Absolute residuals

c) Maximum residual

d) Variance

Correct Answer: a) Sum of squared residuals

Explanation:

Least squares method; unbiased under assumptions.

22. Heteroscedasticity can be addressed by

a) Weighted least squares

b) Increasing sample size

c) Both a and b

d) Adding more variables

Correct Answer: c) Both a and b

Explanation:

Or transformations like log(Y).

23. The Durbin-Watson statistic ranges from

a) 0 to 2

b) 0 to 4

c) -2 to 2

d) 1 to 3

Correct Answer: b) 0 to 4

Explanation:

Around 2 is ideal; <1.5 positive autocorrelation.

24. Multiple R-squared is

a) Same as simple R-squared

b) For multiple predictors

c) Adjusted for df

d) Negative

Correct Answer: b) For multiple predictors

Explanation:

Increases with more variables; use adjusted to compare.

25. Cook's distance measures

a) Influence of observations

b) Linearity

c) Normality

d) Collinearity

Correct Answer: a) Influence of observations

Explanation:

High values (>1) suggest removal or investigation.

26. In forward selection, variables are

a) Added one by one based on significance

b) Removed based on p-value

c) All included

d) Randomly chosen

Correct Answer: a) Added one by one based on significance

Explanation:

Stepwise method; starts with none.

27. The PRESS statistic is used for

a) Model validation via leave-one-out

b) R-squared calculation

c) Slope estimation

d) Intercept

Correct Answer: a) Model validation via leave-one-out

Explanation:

Predicted residual sum of squares.

28. Elastic net combines

a) L1 and L2 penalties

b) Ridge and lasso

c) Both a and b

d) Polynomial and linear

Correct Answer: c) Both a and b

Explanation:

Balances selection and shrinkage.

29. Variance inflation factor for a variable is

a) 1 / (1 - R²) from regression on others

b) R²

c) Tolerance

d) Both a and c

Correct Answer: d) Both a and c

Explanation:

Tolerance = 1 - R²; VIF = 1/tolerance.

30. The hat matrix projects

a) Y onto X space

b) Residuals

c) Leverage

d) All

Correct Answer: a) Y onto X space

Explanation:

H = X(X'X)^{-1}X'; diagonal for leverage.

31. In quantile regression, it estimates

a) Conditional quantiles

b) Mean

c) Median only

d) Variance

Correct Answer: a) Conditional quantiles

Explanation:

Robust to outliers; for heterogeneous effects.

32. The AIC penalizes for

a) Model complexity

b) Sample size

c) Both

d) Goodness of fit

Correct Answer: a) Model complexity

Explanation:

Akaike Information Criterion; lower is better.

33. Generalized linear models (GLM) allow

a) Non-normal responses via link functions

b) Only linear

c) Categorical predictors only

d) Time series

Correct Answer: a) Non-normal responses via link functions

Explanation:

E.g., logit for binary; Poisson for counts.

34. The BIC is similar to AIC but

a) Penalizes more for parameters

b) Ignores n

c) Uses log-likelihood only

d) For large n only

Correct Answer: a) Penalizes more for parameters

Explanation:

Bayesian Information Criterion; stricter for parsimony.

35. In robust regression, it minimizes

a) Huber loss

b) Squared errors

c) Absolute errors

d) All

Correct Answer: a) Huber loss

Explanation:

Less sensitive to outliers than OLS.

36. The partial F-test compares

a) Nested models

b) Non-nested

c) Variances

d) Means

Correct Answer: a) Nested models

Explanation:

For adding variables; hierarchical.

37. Cross-validation in regression assesses

a) Generalization

b) Overfitting

c) Both

d) Linearity

Correct Answer: c) Both

Explanation:

K-fold; average MSE on hold-out.

38. The likelihood ratio test in regression is

a) For nested models

b) Wald test

c) Score test

d) All equivalent

Correct Answer: a) For nested models

Explanation:

Compares -2 log-likelihood.

39. In principal component regression, it uses

a) PCs as predictors

b) Original variables

c) Lasso

d) Ridge

Correct Answer: a) PCs as predictors

Explanation:

Handles multicollinearity by dimension reduction.

40. The mean absolute error (MAE) is

a) Average |residuals|

b) Squared residuals

c) Root squared

d) Percent error

Correct Answer: a) Average |residuals|

Explanation:

Robust to outliers compared to RMSE.

41. Stepwise regression can lead to

a) Overfitting

b) Unstable models

c) Both

d) Underfitting

Correct Answer: c) Both

Explanation:

Automated selection; better to use theory-guided.

42. The variance of the slope estimator is

a) σ² / Σ(X_i - x̄)²

b) σ² / n

c) R² σ²

d) 1 / σ²

Correct Answer: a) σ² / Σ(X_i - x̄)²

Explanation:

Decreases with spread in X.

43. In Poisson regression, the link function is

a) Log

b) Logit

c) Probit

d) Identity

Correct Answer: a) Log

Explanation:

For count data; exp(βX) = λ.

44. The concordance index in survival regression is like

a) R-squared for Cox PH

b) AUC for binary

c) MSE

d) F-stat

Correct Answer: a) R-squared for Cox PH

Explanation:

Proportion of concordant pairs.

45. Bayesian regression incorporates

a) Priors on coefficients

b) Frequentist p-values

c) Only likelihood

d) No uncertainty

Correct Answer: a) Priors on coefficients

Explanation:

Posterior via MCMC or variational.

46. The GAM (Generalized Additive Model) allows

a) Non-linear smooth functions

b) Linear only

c) Categorical only

d) Fixed effects

Correct Answer: a) Non-linear smooth functions

Explanation:

f(X) = β0 + s1(X1) + s2(X2) + ε.

47. In instrumental variables regression, IV addresses

a) Endogeneity

b) Multicollinearity

c) Heteroscedasticity

d) Autocorrelation

Correct Answer: a) Endogeneity

Explanation:

Uses Z correlated with X but not error.

48. The Ljung-Box test in regression residuals checks

a) Autocorrelation

b) Normality

c) Homoscedasticity

d) Linearity

Correct Answer: a) Autocorrelation

Explanation:

For white noise; Q-statistic.

49. Quantile regression at τ=0.5 is

a) Median regression

b) Mean

c) Mode

d) Variance

Correct Answer: a) Median regression

Explanation:

Robust location estimate.

50. The deviance in GLM is analogous to

a) SSE in linear

b) R-squared

c) AIC

d) VIF

Correct Answer: a) SSE in linear

Explanation:

-2 log-likelihood; for model comparison.

51. In ridge, lambda tunes

a) Bias-variance trade-off

b) Overfitting

c) Both

d) Underfitting

Correct Answer: c) Both

Explanation:

Cross-validated; higher lambda more shrinkage.

52. The hat diagonal value is

a) Leverage

b) Cook's D

c) Standardized residual

d) Studentized residual

Correct Answer: a) Leverage

Explanation:

0 < h_ii < 1; average k/n.

53. Negative binomial regression handles

a) Overdispersion in counts

b) Underdispersion

c) Binary

d) Continuous

Correct Answer: a) Overdispersion in counts

Explanation:

Variance > mean; adds dispersion parameter.

54. The Mallow's Cp selects models by

a) Bias + variance estimate

b) R-squared

c) AIC

d) BIC

Correct Answer: a) Bias + variance estimate

Explanation:

Cp ≈ p; for subset selection.

55. In Cox proportional hazards, the assumption is

a) Constant hazard ratio over time

b) Linear time

c) Normal errors

d) Equal variances

Correct Answer: a) Constant hazard ratio over time

Explanation:

Tested with Schoenfeld residuals.

56. The RMSPE is

a) Root mean squared percentage error

b) Residual mean square

c) Percentage R-squared

d) Error variance

Correct Answer: a) Root mean squared percentage error

Explanation:

Scale-free accuracy measure.

57. Backward elimination starts with

a) All variables, removes insignificant

b) None, adds

c) Random

d) Principal components

Correct Answer: a) All variables, removes insignificant

Explanation:

Stepwise; based on p-values.

58. The studentized residual is

a) Residual divided by its SE

b) Leverage-adjusted

c) Both

d) Raw residual

Correct Answer: a) Residual divided by its SE

Explanation:

|e| > 3 flags outliers.

59. In probit regression, the link is

a) Cumulative normal

b) Logit

c) Log

d) Identity

Correct Answer: a) Cumulative normal

Explanation:

For binary; inverse Φ(βX) = P(Y=1).

60. The Vuong test compares

a) Non-nested GLMs

b) Nested

c) Variances

d) Means

Correct Answer: a) Non-nested GLMs

Explanation:

Likelihood-based model selection.

61. Partial regression plots show

a) Marginal effect of X controlling others

b) Total effect

c) Interaction

d) Residual vs fitted

Correct Answer: a) Marginal effect of X controlling others

Explanation:

Residuals of Y on other X vs residuals of this X.

62. The mean squared prediction error is

a) Average (Y - Ŷ)^2 on new data

b) Training MSE

c) R-squared

d) Adjusted R²

Correct Answer: a) Average (Y - Ŷ)^2 on new data

Explanation:

For out-of-sample performance.

63. In ARIMA regression, it models

a) Time-varying errors

b) Static

c) Spatial

d) Categorical

Correct Answer: a) Time-varying errors

Explanation:

Auto-regressive integrated moving average.

64. The concordance correlation coefficient measures

a) Agreement beyond correlation

b) Bias

c) Precision

d) Both b and c

Correct Answer: a) Agreement beyond correlation

Explanation:

ρ_c = ρ / √(1 + bias).

65. Kernel regression is a

a) Non-parametric method

b) Parametric

c) Linear

d) Stepwise

Correct Answer: a) Non-parametric method

Explanation:

Nadaraya-Watson; local weighting.

66. The Ramsey RESET test detects

a) Functional form misspecification

b) Multicollinearity

c) Heteroscedasticity

d) Autocorrelation

Correct Answer: a) Functional form misspecification

Explanation:

Adds powers of fitted values.

67. In survival regression, the baseline hazard is

a) Non-parametric in Cox

b) Parametric

c) Linear

d) Constant

Correct Answer: a) Non-parametric in Cox

Explanation:

h(t|X=0); estimated via Breslow.

68. The MAPE is sensitive to

a) Zero values

b) Outliers

c) Scale

d) Normality

Correct Answer: a) Zero values

Explanation:

Mean absolute percentage error; undefined if Y=0.

69. Best subset selection evaluates

a) All possible subsets

b) Forward only

c) Backward

d) Stepwise

Correct Answer: a) All possible subsets

Explanation:

2^p models; computationally intensive.

70. The externally studentized residual excludes

a) The point itself in SE calculation

b) All points

c) Leverage

d) Intercept

Correct Answer: a) The point itself in SE calculation

Explanation:

For detecting outliers influencing fit.

71. Ordered logit is for

a) Ordinal outcomes

b) Nominal

c) Binary

d) Continuous

Correct Answer: a) Ordinal outcomes

Explanation:

Cumulative logits; proportional odds assumption.

72. The score test in GLM is

a) Efficient under H0

b) Wald

c) LR

d) All same

Correct Answer: a) Efficient under H0

Explanation:

Gradient of log-likelihood; no full fit needed.

73. In spatial regression, SAR models

a) Spatial autocorrelation in errors

b) Lag dependence

c) Both

d) No spatial

Correct Answer: c) Both

Explanation:

Spatial autoregressive; Wy = ρWy + Xβ + ε.

74. The Theil's U statistic compares forecasts to

a) Naive method

b) OLS

c) Ridge

d) Lasso

Correct Answer: a) Naive method

Explanation:

U < 1 better than no-change forecast.

75. LOESS regression uses

a) Local polynomials

b) Global linear

c) Splines

d) Kernels only

Correct Answer: a) Local polynomials

Explanation:

Locally estimated scatterplot smoothing.

76. The Link test in regression checks

a) Omitted variables or specification

b) Multicollinearity

c) Heteroscedasticity

d) Normality

Correct Answer: a) Omitted variables or specification

Explanation:

Regress fitted and squared fitted; significant squared indicates misspec.

77. In accelerated failure time models, it assumes

a) Log-linear effect on time

b) Proportional hazards

c) Weibull distribution

d) Exponential

Correct Answer: a) Log-linear effect on time

Explanation:

log(T) = βX + σW; parametric survival.

78. The SMAPE averages

a) Symmetric absolute percentage errors

b) Squared errors

c) Relative errors

d) Forecast errors

Correct Answer: a) Symmetric absolute percentage errors

Explanation:

Handles zero issues in MAPE.

79. All subset regression is exhaustive but

a) Computationally expensive

b) Fast

c) Approximate

d) Stepwise

Correct Answer: a) Computationally expensive

Explanation:

For p>20, use branch and bound.

80. The deleted residual is

a) Prediction error leaving out i

b) Internal

c) Studentized

d) Leverage

Correct Answer: a) Prediction error leaving out i

Explanation:

PRESS component.

81. Multinomial logit for

a) Nominal outcomes >2 categories

b) Ordinal

c) Binary

d) Continuous

Correct Answer: a) Nominal outcomes >2 categories

Explanation:

One vs all; IIA assumption.

82. The Wald test is

a) Asymptotic for large samples

b) Exact

c) Small sample

d) Non-parametric

Correct Answer: a) Asymptotic for large samples

Explanation:

(β-hat / SE)^2 ~ χ².

83. In SEM, path analysis is

a) Observed variables regression

b) Latent only

c) CFA

d) EFA

Correct Answer: a) Observed variables regression

Explanation:

Special case of SEM without latents.

84. The MASE normalizes errors by

a) In-sample naive forecast

b) Scale

c) Variance

d) SD

Correct Answer: a) In-sample naive forecast

Explanation:

Mean absolute scaled error; scale-free.

85. Smoothing splines minimize

a) RSS + smoothness penalty

b) Only RSS

c) Knots

d) Degrees

Correct Answer: a) RSS + smoothness penalty

Explanation:

λ tunes fit vs smoothness.

86. The CUSUM test detects

a) Structural breaks

b) Autocorrelation

c) Heteroscedasticity

d) Normality

Correct Answer: a) Structural breaks

Explanation:

Cumulative sum of residuals.

87. In frailty models, it accounts for

a) Unobserved heterogeneity

b) Observed covariates

c) Time

d) Censoring

Correct Answer: a) Unobserved heterogeneity

Explanation:

Random effects in survival.

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