The “Recalculate Model” tab includes controls for recalculating and saving the model, and displays a graph plotting the model curve. Clicking on “Calculate Curve” completes the regression based on options set in the other tabs. Note that this may take several minutes depending on the complexity of the data set and options selected.
When complete, the regression plot, equation and other statistics will be displayed. The center red line is the regression model line. If selected, outlier limits, boundaries, and the x-range filter will be plotted. Users can switch between the current tab and “Saved Curve” tab to compare the curve as saved in the database to the newly calculated model. If the newly calculated model is satisfactory, clicking “Save Family Curve” will overwrite the model stored in the database. Leaving the prediction model module and not clicking “Save Family Curve” leaves the family model in the database unchanged.
FAA PAVEAIR uses multiple linear regression techniques to determine the best-fit polynomial for the data. These methods provide an equation for the family curve of the form:
where the values of β are the coefficients of regression, x is pavement age, and y is pavement condition. FAA PAVEAIR uses matrix methods to perform the regression by solving the equation:
where X is a matrix representation of pavement age,
y is a matrix representation of pavement condition, and
Bold values represent
variables that are matrices. FAA PAVEAIR defines
This is required to allow the user to specify the y-intercept of the model (β0). The calculation begins with collecting the condition-age pairs shown in Review Model Data. The user-specified intercept from Options is subtracted from each condition value and the resulting values assembled into a matrix y with size 1 column by n rows, where n is the number of data points. FAA PAVEAIR uses the pavement age values to build matrix X:
where m is the order of polynomial selected in Options. Once
X and y have been constructed, FAA PAVEAIR calculates β0:
The equation form of the solution that describes the family curve is:
