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NZAMT NZQA NZ Grapher NZ Maths Census at School Study It

3.9 Bivariate HOME | Achievement Objectives | Overview | Data sets & Variable Types | Introduction | Scatter plots | Excel | iNZight | Correlation Coefficient & Linear Model | The effect of Groups & Unusual Values | Predictions | Causality | Non-Linear Models | Discussion & Conclusion | Report Writing

Residuals (Extension)

13

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

McDonalds Residuals

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.

 

 

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