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Edexcel IAL Mathematics S3.5 regression and correlation

Practise S3 regression and correlation by ranking paired data, calculating Spearman’s coefficient and testing whether correlation is supported.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
A2

Exam points

  • Calculate Spearman’s rs from ranks and squared rank differences before interpreting association.
  • Test zero or positive correlation by comparing r or rs with the table critical value.
  • Explain tied ranks or choice of correlation method without recalculating when the question asks.

Covered syllabus points

S3.5.1 - Spearman’s rank correlationS3.5.2 - Hypothesis tests for zero correlation

S3.5 - Regression and correlation question 1

[Maximum number: 10]

The table shows the season's best times, x seconds, for the 8 athletes who took part in the 200 m final in the 2021 Tokyo Olympics. It also shows their finishing position in the race.

Table for Question S3.5 - Regression and correlation question 1 — Edexcel A-Level Mathematics A2

Given that the fastest season's best time is ranked number 1

Question (a)

(a)

calculate the value of the Spearman's rank correlation coefficient for these data.

[ 4 ]

Question (b)

(b)

Stating your hypotheses clearly, test, at the 1% level of significance, whether or not there is evidence of a positive correlation between the rank of the season's best time and the finishing position for these athletes.

Chris suggests that it would be better to use the actual finishing time, y seconds, of these athletes rather than their finishing position.

Given that

Sxx=0.1286875Syy=0.55275Sxy=0.225175S_{x x}=0.1286875 \quad S_{y y}=0.55275 \quad S_{x y}=0.225175
[ 4 ]

Question (c)

(c)

Use your value of the product moment correlation coefficient to test, at the 1% level of significance, whether or not there is evidence of a positive correlation between the season's best time and the finishing time for these athletes.

[ 2 ]
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