Data Transformation Data Analysis.

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Presentation transcript:

Data Transformation Data Analysis

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

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.

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.

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.

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

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

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

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.

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