Kenneth ChengMathematical modeling
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Find the fitted slope.

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

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TOPIC 01

Statistical analysis of paired data: mixed review

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

What you will be able to explain

  • Connect the chapter skills without relying on the order of the exercises.

Try it. Leave your reasoning visible.

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

01 / Foundation#Your turn

Find the fitted slope.

Sxx=2,Sxy=48S_{xx}=2,\quad S_{xy}=48
  • Sxx>0; extrapolation beyond observed x needs separate justification and predictions are not certain outcomes.
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.
b=Sxy/Sxxb=S_{xy}/S_{xx}
Worked solution

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

  2. Apply the stated relation and retain its conditions.

    b=48/2=24b=48/2=24

  3. The denominator is the variation in the predictor x.

The requested value is 24.

Checks and common pitfalls: The denominator is the variation in the predictor x.

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

Focus on one question

Teacher preparation and assessment

Question sequence

  • Ask students to name the relevant condition before calculating.

Board plan

  • Compare valid methods and annotate their conditions.

Anticipated thinking

  • A correct final value may still hide a missing assumption.

Assessment checklist

  • Check the method, conditions, reasoning and interpretation separately.

No sign-in. Work stays in this browser. Export before clearing browser data. Written reasoning is assessed with a checklist.

Curriculum and source notes ↗