What happened to the Adjusted R-squared when the categorical variables (promotion_type and season_bucket) were added to the model?

Question

BlackTom AI · Accepted Answer

Adjusted R-squared increased from 0.4892 to 0.8261.

Adjusted R-squared concept and relevance:
Adjusted R-squared measures the proportion of variance explained by the model while penalizing the addition of predictors (it adjusts R-squared for degrees of freedom). Its formula is: R2_adj = 1 - (1 - R2) * (n - 1) / (n - p - 1), where n is sample size and p is number of explanatory variables. An increase in adjusted R-squared means the new predictors improved explanatory power enough to overcome the penalty for extra parameters.

Step-by-step reasoning and calculations:
1. Start values: original adjusted R2 = 0.4892; new adjusted R2 after adding categorical predictors (promotion_type and season_bucket) = 0.8261.
2. Absolute change = 0.8261 − 0.4892 = 0.3369. Showed increase in explained variance after penalization.
3. Relative change (percent increase) = 0.3369 / 0.4892 ≈ 0.6888 → about 68.9% relative increase in adjusted R2.
4. Interpretation: Adding the categorical variables created additional dummy variables (one per category minus baseline), increasing p. Despite this, the model’s R2 increased sufficiently that the adjusted R2 rose from 0.4892 to 0.8261. That indicates the categorical variables provided substantial explanatory information about the dependent variable.

Why the correct answer is correct:
Because adjusted R2 rose by 0.3369, the data show the model fit (after penalizing for extra variables) improved markedly when promotion_type and season_bucket were included. This is exactly what the statement “It increased from 0.4892 to 0.8261.” reports.

Why other possible answers would be incorrect:
- “It decreased” would contradict the computed change (0.8261 > 0.4892).
- “It stayed the same” is incorrect because the numerical values differ.
- “It increased only slightly” is misleading because the increase is large (absolute +0.3369, ~68.9% relative).

Conclusion: The correct answer is that the adjusted R-squared increased from 0.4892 to 0.8261, matching the provided answer.

What happened to the Adjusted R-squared when the categorical variables (promotion_type and season_bucket) were added to the model?Single choice

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