Correlation & Regression (Edexcel International A Level Maths: Statistics 1)

What is the product moment correlation coefficient?

• The product moment correlation coefficient (PMCC) is a way of giving a numerical value to linear correlation of bivariate data
• The PMCC of a sample is denoted by the letter r
  • r can take any value such that 
    • Can be written as 
  • A positive value of r describes positive correlation
  • A negative value of r  describes negative correlation
  • If r = 0 there is no correlation
  • r = 1 means perfect positive correlation and r = -1 means perfect negative correlation
  • The closer to 1 or -1, the stronger the correlation
• The gradient of the regression line does not change the value of r

How is the product moment correlation coefficient (PMCC) calculated?

• For n pairs of bivariate data (x, y) we define the following statistics
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  • These are given in the formula booklet
• These are related to variance and can be written in several different ways:
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• The product moment correlation coefficient (PMCC) is then calculated using the formula
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  • This is given in the formula booklet
    

If the PMCC is close to 1 or -1 then this suggests the data follows a linear model. In this case a regression line of the form y = a + bx is appropriate.

How do I calculate the equation of the regression line of y on x?

• The gradient b of the regression line is calculated using the formula
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  • This is given in the formulae booklet
• The y-intercept a of the regression line is calculated using the formula
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  • This is given in the formulae booklet
  • This is found using the fact that the point  lies on the regression line
• If you are asked to find the equation of the regression line of x on y
  • x = c + dy 
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  • These are not given in the formulae booklet