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      Question

      Assertion (

      • A : A very high R2 value (e.g., 0.98) in a multiple linear regression model always indicates that the model is highly effective for predicting future outcomes and that the chosen independent variables are the true causes of the dependent variable. Reason (
      • R : R2 can be artificially inflated by adding more independent variables to the model, regardless of their actual relevance, or by the presence of data issues like multicollinearity and overfitting. Choose the correct option:
      A Both (A) and (R) are true, and (R) is the correct explanation of (A). Correct Answer Incorrect Answer
      B Both (A) and (R) are true, but (R) is not the correct explanation of (A). Correct Answer Incorrect Answer
      C (A) is true, but (R) is false. Correct Answer Incorrect Answer
      D (A) is false, but (R) is true. Correct Answer Incorrect Answer

      Solution

      Analysis of the Assertion (A) The assertion is false for two primary reasons:

      1. Correlation vs. Causation: R2 measures the proportion of variance in the dependent variable explained by the independent variables. It does not prove a causal relationship.
      2. Predictive Accuracy: A high R2 on training data does not guarantee success with new data. If the model is overfit (too complex for the amount of data), it may have a high R2 but fail miserably when predicting future outcomes.
      Analysis of the Reason (R) The reason is true and highlights why high R2 values can be misleading:
      • Inflated R2: Mathematically, adding any variable to a regression model—even random noise—will either keep the R2 the same or increase it. It will never decrease. This is why "Adjusted R2" is often preferred.
      • Multicollinearity: If independent variables are highly correlated with each other, they can produce a high R2 even if the individual predictors are not statistically significant.
        Key Takeaways for High R2 Values

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