Three scatter diagrams, showing observations from different bivariate data sets, are shown above.
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.
Take logarithms of both sides
Use the addition law for logarithms
Use the power law for logarithms
The graph below shows the distribution of the height, m, of a group of children and the amount of time, hours, they spend napping in the day. It is believed the data can be modelled using the form .
The data are coded using the changes of variables and . The regression line of on is found to be .
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