Regression and Correlation

≈ 25 min

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Regression and Correlation

Correlation $r$ measures strength and direction of linear association, not causation. A least-squares regression line predicts the response variable within the observed range; extrapolation and influential outliers require caution.

Worked reasoning

The magnitude $|r|=0.92$ is close to 1, indicating strong linear association.
The negative sign shows that one variable tends to decrease as the other increases; causation is not established.

Key idea

Correlation describes linear association; it does not establish a causal mechanism.

A dataset has correlation coefficient $r=-0.92$ . Which interpretation is best?

A strong negative linear association

A weak positive association

Proof of negative causation

No association

Which statement best captures the central mathematical idea in Regression and Correlation?

Correlation describes linear association; it does not establish a causal mechanism.

A correlation close to 1 proves that changing one variable causes the other to change.

A memorised formula is valid even when its conditions are not met.

The diagram or notation replaces the need to justify each mathematical step.

When starting a problem about Regression and Correlation, which move is most reliable?

Plot and inspect the data before interpreting $r$ or using a fitted line.

Round every value before identifying the mathematical structure.

Choose the longest available formula and substitute immediately.

Assume the desired conclusion and work backwards without checking equivalence.

Which statement is a misconception that must be rejected when working with Regression and Correlation?

A correlation close to 1 proves that changing one variable causes the other to change.

Correlation describes linear association; it does not establish a causal mechanism.

Plot and inspect the data before interpreting $r$ or using a fitted line.

Inspect residuals, outliers and whether the prediction lies within the data range.

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