MS-DS Master of Data science Statistical Inference & Regression Models 2

Question 1

A researcher fits a multiple linear regression model and finds that adding a 5th predictor increases R² from 0.82 to 0.83 but decreases adjusted R² from 0.81 to 0.80. What does this indicate?

Accepted Answer

The new predictor does not contribute enough to justify its inclusion

Answer

Adjusted R² penalizes unnecessary predictors, so a decrease indicates the added variable does not improve the model enough to offset the loss of a degree of freedom.

Question 2

In hypothesis testing, a p-value of 0.03 is obtained with α = 0.05. Which conclusion is correct?

Accepted Answer

Reject H₀; there is sufficient evidence against it at the 5% level

Answer

Since p = 0.03 < α = 0.05, we reject the null hypothesis at the 5% significance level.

Question 3

Which assumption of OLS regression is violated when the variance of residuals increases with fitted values?

Accepted Answer

Homoscedasticity

Answer

Heteroscedasticity is the violation of the homoscedasticity assumption, where error variance is not constant across levels of the predictors.

Question 4

A 95% confidence interval for a population mean is (12.4, 18.6). What is the correct interpretation?

Accepted Answer

If repeated sampling is used, 95% of similarly constructed intervals will contain the true mean

Answer

Confidence intervals are interpreted in terms of long-run frequency: 95% of intervals constructed with this procedure will capture the true parameter.

Question 5

In logistic regression, the logit function transforms the response variable to:

Accepted Answer

The log of the odds of the outcome

Answer

The logit transformation is log(p/(1-p)), the natural log of the odds, which maps probabilities from (0,1) to (-∞, +∞).

MS-DS Master of Data science Practice Test

MS-DS Master of Data science Practice Test

MS-DS Master of Data science Statistical Inference & Regression Models 2