1.3.3 Coding Bivariate Data

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
$S_{x x}, S_{y y} a n d S_{x y}$ are related to variances so they are affected when the coding involves a multiplication
- $S_{X X} = p^{2} \times S_{x x}$
- $S_{Y Y} = m^{2} \times S_{y y}$
- $S_{X Y} = p m \times S_{x y}$
Coding does not affect the product moment correlation coefficient
- The factors of p and m cancel out in the formula
- $r_{X Y} = r_{x y}$

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

$m = \frac{s - 30000}{12} and w = 52 l$ .

Stewart finds that:

the product moment correlation coefficient between $m$ and $w$ is 0.739,
the equation of the regression line of $m$ on $y$ is $m = - 83.1 + 3.65 w$ .

(a)

Write down the product moment correlation coefficient between

s

and

l

(b)

The equation of the regression line of

s

l

can be written as

s = a + 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

l

can be written as

s = a + b l

. Find the values of

a

and

b

to three significant figures.

1-3-3-coding-bivariate-data-we-solution-part-2

Exam 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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Edexcel International AS Maths: Statistics 1

Revision Notes

1.3.3 Coding Bivariate Data

Coding with PMCC

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

Coding Linear Regression

Does coding affect 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?

Worked Example

Exam Tip

Author: Daniel

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