Coding Bivariate Data (Edexcel International AS Maths: Statistics 1): Revision Note

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

• $S_{xx},S_{yy}and{S}_{xy}$ are related to variances so they are affected when the coding involves a multiplication

  • $S_{XX}=p^2\times S_{xx}$

  • $S_{YY}=m^2\times S_{yy}$

  • $S_{XY}=pm\times S_{xy}$

• Coding does not affect the product moment correlation coefficient

  • The factors of p and m cancel out in the formula

  • $r_{XY}=r_{xy}$

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