LEARN · EXPLAIN · REVISE

Find r from centered summaries.

Read the idea, work independently, then explain what changed.

TOPIC 01

Statistical analysis of paired data: mixed review

A mixed assessment: identify the method, justify it and revise your reasoning.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Foundation#Your turn

S_{xx}=4,\quad S_{yy}=400,\quad S_{xy}=20

Both centered sums of squares must be positive; correlation measures linear association and does not establish causation.

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Use the paired-data summaries, preserving which observations belong together.

Hint 2

Use this intermediate relation.

r=S_{xy}/\sqrt{S_{xx}S_{yy}}

Worked solution

The requested value is 0.5.

Checks and common pitfalls: The positive square root gives the denominator scale.

Think first. Reveal a hint when the class is ready.

Teacher preparation and assessment