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# Residuals (Extension)

 Scatterplot Residuals The difference between an actual data value (point on the scatterplot) and the predicted value (corresponding point on the line of best fit) is called the residual Calculation of the residual Plotting of the residual If there is a pattern seen in the residual plot then this shows features of the data and if another model is a better fit Class Exemplar: Hawai'i Island Chain: Data csv, Information page | Google Doc write up Class Exemplar: American New Cars 1993 Data csv, Information pdf | Google Doc write up

 Linear regression relationship = linear trend + scatter Residual = observed y – predicted Aim: Sum of squares of residual minimised          Least Squares regression line Σ(residuals) = 0 Σ(residuals)2 minimised Mean point on regression line Constructing a graph of the residuals is an excellent way to establish if the linear model is an appropriate model for the bivariate data. Using Excel Data Analysis Toolpack to produce residual graphs Read Sigma pg 283 Excel demonatration of residuals What does this graph show? It gives a clear indication if a linear model is appropriate for data. If the residual data points are scattered above and below the 'x' axis then a linear model is appropriate. If there is a pattern to the residual scatter plot then a different model may be better model.