Mean absolute error averages the absolute differences between observed and predicted values. It is expressed in the same units as the response and is less sensitive to large errors than squared-error metrics.
Correct Answer: B. It penalizes adding predictors that provide little improvement
Explanation:
Ordinary R² cannot decrease when predictors are added, even if they are unhelpful. Adjusted R² accounts for model size and sample size when assessing improvement.
Correct Answer: B. The proportion of response variation explained by the model relative to a mean-only baseline
Explanation:
R² compares the model’s squared error with the total variation around the response mean. A high value indicates strong in-sample explanatory fit, not guaranteed generalization or causation.
Correct Answer: A. It supports common small-sample confidence intervals and significance tests
Explanation:
Normal-error assumptions justify exact forms of several classical inferential procedures. Point predictions can still be computed when residuals are not perfectly normal.
Repeated measurements on one patient are often correlated because they share individual characteristics. Ignoring this dependence can make uncertainty estimates misleading.
Correct Answer: D. Squaring prevents positive and negative errors from canceling and penalizes large errors more
Explanation:
Raw residuals can sum near zero even when predictions are poor because their signs differ. Squared residuals are nonnegative and make large deviations especially costly.
Least squares measures each prediction error, squares it, and minimizes the total. Squaring gives larger errors more influence and yields a tractable optimization problem.
Correct Answer: D. The predicted response when the predictor equals zero
Explanation:
The intercept is where the fitted line crosses the response axis at x = 0. Its practical meaning depends on whether zero is a sensible predictor value.
Correct Answer: C. Each additional thousand rupees is associated with an average sales increase of 4.2 units
Explanation:
The slope is the expected change in the predicted response for a one-unit increase in the predictor. The interpretation is associational unless the study design supports a causal claim.
Simple linear regression expresses the response as an intercept plus a slope times one predictor and an error term. The error represents variation not explained by the line.
