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# Further8 data transformation

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### Further8 data transformation

1. 1. Further MathsData Transformation K McMullen 2012
2. 2. Data TransformationsWhen a scatterplot is non-linear we can linearise theregression line by transforming the data using one ofthe following transformations: Squared transformation Log transformation Reciprocal transformationAlways use the table of transformations to help youchoose the right transformationsOnce you have chosen your transformations, the onewith the highest r2 value is the best transformationgiven that it’s residual plot is randomly scattered(which should be the case is r2 is high) K McMullen 2012
3. 3. Data TransformationsSquared transformations Has the effect of decreasing values less than 1 and increasing values greater than 1 The effect of the squared transformation is to stretch the valuesExample of x2 transformation:Example of y2 transformation: K McMullen 2012
4. 4. Data TransformationsLog transformation: reduces all values, andvalues between 0 and 1 become negativeLarge values are reduced much more than smallvaluesThe effect of the log transformation is tocompress the values Example of a log (x) transformation: Example of a log (y) transformation: K McMullen 2012
5. 5. Data TransformationsReciprocal transformations: reduces all valuesgreater than 1Large values are reduced much more than smallvaluesThe effect of the reciprocal transformation is tocompress the large values to and even greaterextent than the log transformationExample of a 1/x transformation:Example of a 1/y transformation: K McMullen 2012
6. 6. Data TransformationsTo do a transformation: Draw your scatterplot Look at the table of transformations to decide which transformations to try For each transformation: Transform your x or y values depending on the transformation Calculate the r2 value for each transformation Draw the residual graph against your x values (if you transformed x then you use the transformed values) for each transformation and comment (remember that residual values are always on your y-axis) Compare each transformation and decide which is best When writing your equation make sure you use the transformed variable in your answer and calculations K McMullen 2012