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?
✅ 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
✅ 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
✅ 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
✅ Correct Answer: b) Relationship between X and Y is linear
📝 Explanation:
Verified via scatter plots or residual plots.
5. Homoscedasticity refers to
✅ Correct Answer: a) Constant variance of residuals
📝 Explanation:
Tested with Breusch-Pagan; violations suggest heteroscedasticity.
6. In multiple regression, multicollinearity is detected using
✅ Correct Answer: a) VIF (Variance Inflation Factor)
📝 Explanation:
VIF > 5-10 indicates high collinearity among predictors.
7. The intercept in regression is
✅ Correct Answer: a) Expected Y when all X=0
📝 Explanation:
β0; may lack interpretation if X=0 is outside range.
8. Residuals are
✅ Correct Answer: b) Observed minus predicted values
📝 Explanation:
Used for diagnostics; should be randomly distributed.
9. The F-test in regression tests
✅ Correct Answer: a) Overall model significance
📝 Explanation:
H0: all β=0; low p-value indicates model explains variance.
10. t-test for coefficients tests
✅ Correct Answer: a) H0: β=0
📝 Explanation:
Significance of individual predictors.
11. Adjusted R-squared accounts for
✅ Correct Answer: c) Both a and b
📝 Explanation:
Penalizes adding irrelevant variables; better for model comparison.
12. Outliers in regression can be detected using
✅ Correct Answer: a) Leverage and Cook's distance
📝 Explanation:
High values indicate influential points affecting fit.
13. The standard error of the estimate is
✅ Correct Answer: a) Root mean squared error
📝 Explanation:
Measures prediction accuracy; √(SSE/(n-k-1)).
14. Autocorrelation in residuals is tested with
✅ Correct Answer: a) Durbin-Watson test
📝 Explanation:
Values near 2 indicate no serial correlation; common in time series.
15. Logistic regression is used for
✅ Correct Answer: b) Binary or categorical outcomes
📝 Explanation:
Models log-odds; uses sigmoid function.
16. In ridge regression, the penalty is on
✅ Correct Answer: a) Sum of squared coefficients
📝 Explanation:
L2 regularization; reduces multicollinearity.
17. Lasso regression uses
✅ Correct Answer: a) L1 penalty
📝 Explanation:
Sum of absolute coefficients; performs variable selection.
18. Polynomial regression extends linear by
✅ Correct Answer: a) Adding higher powers of X
📝 Explanation:
Captures non-linear relationships; risks overfitting.
19. The coefficient of determination is
✅ Correct Answer: a) R-squared
📝 Explanation:
1 - (SS_res / SS_tot).
20. Normality of residuals is tested with
✅ 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
✅ Correct Answer: a) Sum of squared residuals
📝 Explanation:
Least squares method; unbiased under assumptions.
22. Heteroscedasticity can be addressed by
✅ Correct Answer: c) Both a and b
📝 Explanation:
Or transformations like log(Y).
23. The Durbin-Watson statistic ranges from
✅ Correct Answer: b) 0 to 4
📝 Explanation:
Around 2 is ideal; mean; adds dispersion parameter.
24. The Mallow's Cp selects models by
✅ Correct Answer: a) Bias + variance estimate
📝 Explanation:
Cp ≈ p; for subset selection.
25. In Cox proportional hazards, the assumption is
✅ Correct Answer: a) Constant hazard ratio over time
📝 Explanation:
Tested with Schoenfeld residuals.
26. The RMSPE is
✅ Correct Answer: a) Root mean squared percentage error
📝 Explanation:
Scale-free accuracy measure.
27. Backward elimination starts with
✅ Correct Answer: a) All variables, removes insignificant
📝 Explanation:
Stepwise; based on p-values.
28. The studentized residual is
✅ Correct Answer: a) Residual divided by its SE
📝 Explanation:
|e| > 3 flags outliers.
29. In probit regression, the link is
✅ Correct Answer: a) Cumulative normal
📝 Explanation:
For binary; inverse Φ(βX) = P(Y=1).
30. The Vuong test compares
✅ Correct Answer: a) Non-nested GLMs
📝 Explanation:
Likelihood-based model selection.
31. Partial regression plots show
✅ Correct Answer: a) Marginal effect of X controlling others
📝 Explanation:
Residuals of Y on other X vs residuals of this X.
32. The mean squared prediction error is
✅ Correct Answer: a) Average (Y - Ŷ)^2 on new data
📝 Explanation:
For out-of-sample performance.
33. In ARIMA regression, it models
✅ Correct Answer: a) Time-varying errors
📝 Explanation:
Auto-regressive integrated moving average.
34. The concordance correlation coefficient measures
✅ Correct Answer: a) Agreement beyond correlation
📝 Explanation:
ρ_c = ρ / √(1 + bias).
35. Kernel regression is a
✅ Correct Answer: a) Non-parametric method
📝 Explanation:
Nadaraya-Watson; local weighting.
36. The Ramsey RESET test detects
✅ Correct Answer: a) Functional form misspecification
📝 Explanation:
Adds powers of fitted values.
37. In survival regression, the baseline hazard is
✅ Correct Answer: a) Non-parametric in Cox
📝 Explanation:
h(t|X=0); estimated via Breslow.
38. The MAPE is sensitive to
✅ Correct Answer: a) Zero values
📝 Explanation:
Mean absolute percentage error; undefined if Y=0.
39. Best subset selection evaluates
✅ Correct Answer: a) All possible subsets
📝 Explanation:
2^p models; computationally intensive.
40. The externally studentized residual excludes
✅ Correct Answer: a) The point itself in SE calculation
📝 Explanation:
For detecting outliers influencing fit.
41. Ordered logit is for
✅ Correct Answer: a) Ordinal outcomes
📝 Explanation:
Cumulative logits; proportional odds assumption.
42. The score test in GLM is
✅ Correct Answer: a) Efficient under H0
📝 Explanation:
Gradient of log-likelihood; no full fit needed.
43. In spatial regression, SAR models
✅ Correct Answer: c) Both
📝 Explanation:
Spatial autoregressive; Wy = ρWy + Xβ + ε.
44. The Theil's U statistic compares forecasts to
✅ Correct Answer: a) Naive method
📝 Explanation:
U < 1 better than no-change forecast.
45. LOESS regression uses
✅ Correct Answer: a) Local polynomials
📝 Explanation:
Locally estimated scatterplot smoothing.
46. The Link test in regression checks
✅ Correct Answer: a) Omitted variables or specification
📝 Explanation:
Regress fitted and squared fitted; significant squared indicates misspec.
47. In accelerated failure time models, it assumes
✅ Correct Answer: a) Log-linear effect on time
📝 Explanation:
log(T) = βX + σW; parametric survival.
48. The SMAPE averages
✅ Correct Answer: a) Symmetric absolute percentage errors
📝 Explanation:
Handles zero issues in MAPE.
49. All subset regression is exhaustive but
✅ Correct Answer: a) Computationally expensive
📝 Explanation:
For p>20, use branch and bound.
50. The deleted residual is
✅ Correct Answer: a) Prediction error leaving out i
📝 Explanation:
PRESS component.
51. Multinomial logit for
✅ Correct Answer: a) Nominal outcomes >2 categories
📝 Explanation:
One vs all; IIA assumption.
52. The Wald test is
✅ Correct Answer: a) Asymptotic for large samples
📝 Explanation:
(β-hat / SE)^2 ~ χ².
53. In SEM, path analysis is
✅ Correct Answer: a) Observed variables regression
📝 Explanation:
Special case of SEM without latents.
54. The MASE normalizes errors by
✅ Correct Answer: a) In-sample naive forecast
📝 Explanation:
Mean absolute scaled error; scale-free.
55. Smoothing splines minimize
✅ Correct Answer: a) RSS + smoothness penalty
📝 Explanation:
λ tunes fit vs smoothness.
56. The CUSUM test detects
✅ Correct Answer: a) Structural breaks
📝 Explanation:
Cumulative sum of residuals.
57. In frailty models, it accounts for
✅ Correct Answer: a) Unobserved heterogeneity
📝 Explanation:
Random effects in survival.
