1. Data Transformation
Data Analysis

2. Residual Analysis
From: Jones et al., (2012) Essential Further Mathematics 4E, pg 132

3. Residual
Actual y value – predicted y value = residual Actual y value comes from the scatterplot. It is from the actual data. Predicted y value comes from the equation. It is a theoretical value. When we add all of the residuals from a least squares regression they should add to zero, or very close to zero.

4. From: MathsQuest 12 Further Mathematics VCE Units 3 and 4 (5E) by Barnes, Nolan and Phillips, pg 145
Residual Plot
Plots the residuals against the original x values. If the residuals are randomly scattered then we probably have a linear relationship. If they form a pattern, such as a curve, they probably form a non-linear relationship. Page 168 of the calculator notes explain how to do a residual plot.

5. From: MathsQuest 12 Further Mathematics VCE Units 3 and 4 (5E) by Barnes, Nolan and Phillips, pg 149
Transforming data
If the data is non-linear we may be able to transform it and force it to be linear. See the Transforming to Linearity Interactivity in eBookPLUS.

6. Logarithmic and Reciprocal Transformations
From: MathsQuest 12 Further Mathematics VCE Units 3 and 4 (5E) by Barnes, Nolan and Phillips, pg 150
Logarithmic and Reciprocal Transformations

7. Quadratic Transformations
From: MathsQuest 12 Further Mathematics VCE Units 3 and 4 (5E) by Barnes, Nolan and Phillips, pg 150
Quadratic Transformations

8. From: Jones et al., (2012) Essential Further Mathematics 4E, pg 190

9. Which transformation do I choose?
The best transformation will be the one with r = +/- 1. The closer to 1 (or -1) the better the transformation. You should try all transformation for the appropriate quadrant in the circle of transformations before making your choice.

10. If your data is non-linear you will also need to transform the data using the correct methods and choose the best model.
From: Jones et al., (2012) Essential Further Mathematics 4E, pg 140