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International A LevelMaths: Statistics 1EdexcelRevision Notes1. Data Presentation & Interpretation1.3 Correlation & Regression1.3.3 Coding Bivariate Data

Coding Bivariate Data (Edexcel International A Level Maths: Statistics 1)

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Dan

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Dan

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Coding with PMCC

Does coding affect the product moment correlation coefficient (PMCC)?

  • We can code data using linear transformations
    • X = px + q
    • Y = my + n
      • The new variables won't necessarily be the upper case versions of the old variables - they could be any letter
  • begin mathsize 16px style S subscript x x end subscript comma S subscript y y end subscript space a n d space S subscript x y end subscript end style are related to variances so they are affected when the coding involves a multiplication
    • begin mathsize 16px style S subscript X X end subscript equals p squared cross times S subscript x x end subscript end style
    • size 16px S subscript Y Y end subscript size 16px equals size 16px m to the power of size 16px 2 size 16px cross times size 16px S subscript y y end subscript
    • begin mathsize 16px style S subscript X Y end subscript equals p m cross times S subscript x y end subscript end style
  • Coding does not affect the product moment correlation coefficient
    • The factors of p and m cancel out in the formula
    • begin mathsize 16px style r subscript X Y end subscript equals r subscript x y end subscript end style

Coding Linear Regression

Does coding affect the equation of the regression line of y on x?

  • Coding does affect the equation of the regression line of y on x
  • Coding is used to make numbers simpler to work with
  • The equation of the regression line of Y on X can be calculated using the coded data
  • This equation can then be used to find the equation of the regression line of y on x

How do I use coding to find the equation of the regression line of y on x?

  • Given the variables x and y are coded using
    • X = px + q
    • Y = my + n
  • The equation of the regression line of Y on X can be calculated as Y = A + BX
  • To find the equation of the regression line of y on x
    • Substitute the codes into the equation
      • my + n = A + B(px + q)
    • Rearrange into the form y = a + bx

Worked example

Stewart collects data to compare the salaries, £s , and lengths of service, l years, of employees in a business. Stewart codes the data using the formulae

 m equals fraction numerator s minus 30000 over denominator 12 end fraction space and space w equals 52 l.

Stewart finds that:

  • the product moment correlation coefficient between m and w is 0.739,
  • the equation of the regression line of mon y is m equals negative 83.1 plus 3.65 w. 
(a)
Write down the product moment correlation coefficient between s and l.

 

(b)
The equation of the regression line of s on l can be written as s equals a plus b l. Find the      values of a and b to three significant figures.
(a)
Write down the product moment correlation coefficient between s and l.

1-3-3-coding-bivariate-data-we-solution-part-1

(b)
The equation of the regression line of s on l can be written as s equals a plus b l. Find the      values of a and b to three significant figures.
1-3-3-coding-bivariate-data-we-solution-part-2

Examiner Tip

  • When rearranging the equation of the regression it is important that you don’t round your coefficients until the very end. Use your ANS button on your calculator to keep the accuracy.

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    Previous:1.3.2 Correlation & RegressionNext:2.1.1 Calculating Probabilities & Events
    Dan

    Author: Dan

    Expertise: Maths

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.