What is Pearson’s product-moment correlation coefficient?

• Pearson’s product-moment correlation coefficient (PMCC) is a way of giving a numerical value to a?linear relationship?of bivariate data
• 
  • A?positive value?of?r?describes?positive correlation
  • A?negative value?of?r?describes?negative correlation
  • r?= 0 means there is?no linear correlation
  • r?= 1 means?perfect positive linear?correlation
  • r?= -1 means?perfect negative linear?correlation
  • The closer to 1 or -1 the stronger the correlation

How do I calculate Pearson’s product-moment correlation coefficient (PMCC)?

• You will be expected to use the statistics mode on your GDC to calculate the PMCC
• The formula can be useful to deepen your understanding

• • You?do not need to learn this?as using your GDC will be expected

When does the PMCC suggest there is a linear relationship?

• Critical values?of?r?indicate when the PMCC would suggest there is a linear relationship
  • In your exam you will be given critical values where appropriate
  • Critical values will depend on the size of the sample
• If the?absolute value?of the?PMCC?is?bigger?than the?critical value?then this suggests a linear model is appropriate

What is linear regression?

• If?strong linear correlation?exists on a scatter diagram then the data can be modelled by a?linear model
  • Drawing lines of best fit by eye is not the best method as it can be difficult to judge the best position for the line
• The?least squares regression line?is the line of best fit that minimises the?sum of the squares?of the gap between the line and each data value
• It can be calculated by either looking at:
  • vertical distances?between the line and the data values
    • This is the?regression line of?y?on?x
  • horizontal distances?between the line and the data values
    • This is the?regression line of?x?on?y

How do I find the regression line of?y?on?x?

How do I find the regression line of?x?on?y?

How do I use a regression line?

• The regression line can be used to decide what type of correlation there is if there is no scatter diagram
  • If the gradient is?positive?then the data set has?positive correlation
  • If the gradient is?negative?then the data set has?negative correlation
• The regression line can also be used to?predict?the value of a?dependent variable?from an?independent variable
  • The equation for the?y?on?x?line should only be used to make predictions for?y
    • Using a?y?on?x?line to predict?x?is not always reliable
  • The equation for the?x?on?y?line should only be used to make predictions for?x
    • Using an?x?on?y?line to predict?y?is not always reliable
  • Making a prediction within the range of the given data is called?interpolation
    • This is usually reliable
    • The stronger the correlation the more reliable the prediction
  • Making a prediction outside of the range of the given data is called?extrapolation
    • This is much less reliable
  • The prediction will be more reliable if the number of data values in the original sample set is bigger