This tool implements Ordinary Least Squares regression algorithm on the dataset of the selected layer. It produces a linear regression model from the selected attributes to display the relationships between the dependent and explanatory variables.
The Spatial Prediction-OLS tool can be selected by navigating the following path:
Tools > Vector Processing > Statistical Analysis > Spatial Prediction-OLS
The first section requires you to select the data layers and parameters required to run the Spatial Prediction tool.
- Select Layer Layer on which you will run this tool.
- Dependent Variable Attribute that is to be predicted.
- Explanatory Variable Attributes to be analyzed in relationship with the dependent variable.
Once you decide all the variables required, then click Run. This produces a window that displays summary of all the computed metrics needed for the regression model. Some of the key statistic factors in linear regression are defined as below:
Model Metrics
Adj R-Squared - Modified version of R-Squared that is adjusted to represent the number of predictors in the model. This metric is used to determine the accuracy of the model. The closer it is to one, the more accurate it is.
F-Statistic - Represents the statistical significance of the explanatory variables in predicting the value of the dependent variable.
Omnibus - Represents the normalcy of the distribution. Zero indicates perfect normalcy.
Prob (Omnibus) - Measurement of the probability that the values are normally distributed. The perfect value for this indicator is one.
Skew - Measurement of symmetry in the data. The ideal value for this metric is zero. This metric is important as it provides useful indicators about the data from its distribution.
Kurtosis - This indicator represents peaks of data or concentration of data points around zero in a normal curve. As the value for this indicator increases, the probability of outliers in the dataset decreases.
Durbin-Watson - Used to indicate the autocorrelation among the prediction errors in the model. Autocorrelation is the degree of coordination between different variables across successive time intervals.
Jarque-Bera (JB) - Indicates if the residuals (prediction errors) are normally distributed or not to the assess model bias.
Cond. No. – Measurement of the model's sensitivity as compared to the size of changes in the data being analyzed.
Coefficient Metrics
Coefficient[a] - Represents the strength/weight and type of relationship the variable has with the dependent attribute.
StdError - This value is the measurement of the variation in the coefficient across different data points. It represents the distance between the observed value from its corresponding point in the regression line.
t-Statistic - This value represents the coefficient divided by the standard error.
Probability[b] - This indicator is a measurement of how accurately the coefficient is produced through the model by chance.
You can analyze these values to determine if the model developed is efficient enough to use. Alternatively, this window can also be exported into a PDF file by clicking on the top right icon.
Once you are satisfied with the metrics, click on Agree and Proceed. This produces the visual representation of the predicted data.
You can view the output after storing it. To save the output, you must enter the Output Layer Name and click on Save Data button. The saved output will be added as a new layer in the current map session, where you can apply styling as required. This output layer will also be available in 'My Data' section and can be used in any map session of interest.