# Spatial Lag Residual Plot

## Introduction

The residual plot is a graph that displays residual value or the difference between the observed value of the dependent variable ($$y$$) and the predicted value ($$\hat{y}$$). It is used to check for fitness of the spatial lag model. More discussion and explanation of spatial lag models can be found here.

## Inputs

To show the model in action, we will run the tool looking at a spatial lag model of effect of income on rent across Melbourne. In doing so, we assume that the Lagrange Multipliers test has indicated that a spatial lag model is the appropriate treatment for this dataset, as opposed to the Spatial Error Model.

Once you have done this, open the Spatial Lag Residual Plot (Tools → Charts → Spatial Lag Residual Plot) and enter the parameters as shown in the image below (these are explained in more detail after the image)

[Click to Enlarge]

• Dataset Input: Select the spatialised dataset for which you would like to generate the graph. In this instance we select SPATIALISED SA2-based T02 Selected Medians and Averages as at 2011-08-11
• Spatial Weights Matrix: Select the spatial weights matrix that you generated which will be used to feed into the spatial lag model. In this instance we select CONTIG SWM FOR SPATIALISED SA2-based T02 Selected Medians and Averages as at 2011-08-11
• Key Column: Select the column in the spatialised dataset which specifies the unique codes for your areas. In this instance we select ASGS 2011
• Dependent Variable: Select the variable that you would like to be explained by the model (i.e. the Y variable). In this instance we select Median rent ($/weekly) • Independent Variables: Select the variables that you would like to test as explanatory variables for the variation in Y (i.e. the X variables). You can select more than one, although in this instance, we are selecting only Median total family income ($/weekly)
• Chart Title: Create a name for your graph. In this instance we have called the graph SPATIAL LAG RESIDUAL PLOT Median Income vs Median Rent Adelaide SA2s
• Grid: Keep this checked if you want grid lines on the graph (default), or unchecked if you want it clear
• Greyscale: Keep this unchecked if you want a colour graph (default) or checked if you want it to be greyscale

Once you have added all the parameters, click Add and Run to execute the tool

## Outputs

Once your tool has run, click the Display button on the pop up dialogue box that appears. Your graph should look something like the image shown below

[Click to Enlarge]

## References

1. Cressie, N. A. C. (1991) Statistics for spatial data, New York: Wiley.
2. Olive, D. J. (2013) Plots, Prediction and Testing for the Multivariate Linear Model, preprint, see (http://lagrange.math.siu.edu/Olive/ppmultreg.pdf ).
3. Hofe, R. (2010) Residual plot, N. Salkind (Ed.), Encyclopedia of research design, pp. 1263 – 1268, Thousand Oaks, CA: SAGE Publications, Inc.