Assertion (A): A very high R2 value (e.g., 0.98) in a

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.

• 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.