MS-DS Master of Data science Statistical Inference & Regression Models 3 — Questions and Answers
Question 1: Which test is most appropriate for comparing the means of three or more independent groups?
- Paired t-test
- Two-sample z-test
- One-way ANOVA F-test (Correct answer)
- Chi-square goodness-of-fit test
Correct answer: One-way ANOVA F-test
One-way ANOVA tests whether at least one group mean differs from the others by comparing between-group and within-group variance.
Question 2: In ridge regression, the regularization parameter λ controls:
- The number of predictors selected
- The degree of shrinkage applied to regression coefficients (Correct answer)
- The transformation applied to the response variable
- The threshold for statistical significance
Correct answer: The degree of shrinkage applied to regression coefficients
Ridge regression adds an L2 penalty (λΣβ²) to the loss function, shrinking coefficients toward zero as λ increases.
Question 3: A Type II error in hypothesis testing occurs when:
- A true null hypothesis is rejected
- A false null hypothesis is not rejected (Correct answer)
- The significance level is set too low
- The sample size is too large
Correct answer: A false null hypothesis is not rejected
Type II error (false negative) is failing to reject H₀ when H₀ is actually false; its probability is denoted β.
Question 4: The coefficient of determination R² in a simple linear regression equals 0.64. What does this mean?
- The correlation coefficient between X and Y is 0.64
- 64% of the variance in Y is explained by X (Correct answer)
- The regression slope is 0.64
- The model correctly classifies 64% of observations
Correct answer: 64% of the variance in Y is explained by X
R² measures the proportion of total variance in the dependent variable explained by the regression model.
Question 5: In a Poisson regression model, the canonical link function is:
- The logit link
- The identity link
- The log link (Correct answer)
- The probit link
Correct answer: The log link
Poisson regression uses the natural log as its canonical link function, modeling log(μ) as a linear combination of predictors.
Question 6: The power of a statistical test is defined as:
- 1 minus the probability of a Type I error
- The probability of rejecting H₀ when H₁ is true (Correct answer)
- The probability of accepting H₀ when it is true
- The effect size divided by sample size
Correct answer: The probability of rejecting H₀ when H₁ is true
Power = 1 - β = P(reject H₀ | H₁ is true), representing the test's ability to detect a true effect.
Question 7: In a simple linear regression, which diagnostic plot is most useful for detecting non-linearity?
- Normal Q-Q plot of residuals
- Residuals vs. fitted values plot (Correct answer)
- Scale-location plot
- Cook's distance plot
Correct answer: Residuals vs. fitted values plot
A residuals vs. fitted values plot reveals non-random patterns that indicate non-linearity in the relationship between predictors and response.
MS-DS Master of Data science Statistical Inference & Regression Models 3
Which test is most appropriate for comparing the means of three or more independent groups?