AQA A Level Maths: Statistics复习笔记2.5.1 PMCC & Non-linear Regression

Product Moment Correlation Coefficient (PMCC)

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
  • 2-5-1-pmcc-diagram-1

Worked Example

2-5-1-pmcc-we-solution

Non-linear Regression

At AS Level you learned how to use linear regression models to describe a relationship between two variables. However, it is possible for two variables to have a relationship that does not fit a linear model, but still shows a pattern based on exponential growth or decay. A linear regression model is only appropriate if the PMCC is close to 1 or -1.

What forms can non – linear regression models take?

  • If a bivariate data set appears to have a non – linear relationship it could fit an exponential model

How can non – linear regression models be used?

  • Non – linear regression models can be used in much the same way as linear regression models
  • By coding the original data using logarithms (changing the variables) a regression line of Y on X can be found
    • This can be used to make predictions for data values that are within the range of the given data (interpolation)
    • Making a prediction outside of the range of the given data is called extrapolation and should not be done

Worked Example

2-5-1-non-linear-regression-we-solution-2-part-1

Uo6sLrf6_2-5-1-non-linear-regression-we-solution-2-part-21

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