LEARN · EXPLAIN · REVISE

For pairs (−1,t),(0,0),(1,t), find Sxy.

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 / Standard#Your turn

t=26

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.

\bar x=0;\quad S_{xy}=\sum x_i(y_i-\bar y)

Worked solution

Use the paired-data summaries, preserving which observations belong together.
Apply the stated relation and retain its conditions.
$S_{xy}=-1(26-52/3)+1(26-52/3)=0$
Symmetry cancels the centered products even though the pattern is nonlinear.

The requested value is 0.

Checks and common pitfalls: Symmetry cancels the centered products even though the pattern is nonlinear.

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

Teacher preparation and assessment