Correlation and Regression

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Correlation and Regression

• 2July Presentation
• AS Mathematics
• Statistics 1 Module

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Introduction

• A scatter diagram is usually used to see if there
  is a relationship between two variables
• This relationship is described as a correlation
• In Statistics 1 you will only consider linear
  relationships where the correlation will be
  positive or negative

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Correlation

• The linear correlation of a scatter graph can be
  quantified by calculating the Product Moment
  Correlation Coefficient (PMCC)
• The PMCC r sxy , and ranges from -1 ? r ?
  1 ?sxxsyy
• Values of PMCC
• Guessing PMCC
• Calculating PMCC

4
Correlation Practice

• Question 1
• Question 2

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Regression

• As well as describing the type of correlation
  that may exist between two variables, it is also
  possible to find the regression line for that
  scatter diagram (line of best fit)
• When you have two variables it is usual to assign
  on to be the explanatory variable (independent, x
  values) - the variable that you have some control
  over - and one to be the response variable
  (dependent, y values) - the one you measure that
  changes because of the explanatory variable
• When calculating a line of best fit in this way,
  you will work out y a bx where y is the
  predicted value for a give x value (this is
  regressing y on x)

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Regression Calculations

• Fitting a line on to a scatter diagram involves
  finding the best possible position so the the
  line reduces the residuals (errors) from the
  predicted line to the actual y values
• One method to use is known as the least square
  method
• This calculates the smallest sum of square
  residuals for a given line (why square ?)
• y on x
• line of best fit
• least squares method

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Calculating the regression line

• The regression line for y on x is given as
  y a bx
  _ _ where b sxx and a y -
  bx sxy
• Question 1
• Question 2
• (a more difficult question - using coding)

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Check your understanding

• Correlation and Regression quiz