The closer that the value of R2 is to 1, we would expect:

Question

BlackTom AI · Accepted Answer

When evaluating what a higher R^2 implies, think about the meaning of the coefficient of determination. R^2 measures how much of the variability in the dependent variable is explained by the regression model. A value near 1 indicates that most of the observed variation is captured by the regression line, leaving only small residuals. Consequently, the data points should align more tightly with the fitted line, reducing scatter around it. Now, in this specific question, there is only one available answer statement: 'Our observed data to be closer to the regression line.' This aligns with the interpretation of a high R^2, since a strong fit means data points cluster near the line.

However, there are no other answer options provided to compare against, so we cannot evaluate alternative claims or common misconceptions (such as overfitting, misinterpretation of correlation as causation, or implying causality from a high R^2). Without additional choices, the analysis is limited to confirming the intuition that R^2 approaching 1 signals better alignment of data with the regression line, i.e., reduced unexplained variance.

To summarize in a single idea: a larger R^2 (closer to 1) corresponds to observations lying closer to the regression line, which is exactly what the provided option states.

PSYC20009_2025_SM2 Quiz for Simple Linear Regression: Part 2

The closer that the value of R2 is to 1, we would expect:

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