CFLib.org – Common Function Library Project

Description:
This function calculates a best fit line for a given set of points (i.e., provides slope & intercept) and predicts a future value along a linear trend. It also provides values for a number of residual functions (SSR, SSE, MSE, Pearson's R, max absolute residual) and provides residual values for all given data points. Enter points as comma-delimited lists of X and Y values. Enter a known X for the third argument to get a predicted y value.

Return Values:
Returns a struct.

Example:

<cfoutput>For the following data points: (1, 3513.99) (30, 3488.04) (60, 2649.84) (90, 4444.05) (120, 4411.23), find the expected y value of (150, y).</cfoutput>
<cfset xlist="0, 30, 60, 90, 120">
<cfset ylist="3513.99, 3488.04, 2649.84, 4444.05, 4411.23"> 
<cfset myforecast = #forecast(Xlist, Ylist, 150)#>
<cfoutput><br>Y is: #myforecast[1][1]#</cfoutput>
<cfdump var="#forecast(Xlist, Ylist, 150)#" >

Parameters:

Full UDF Source:

/**
 * Performs a number of statistical functions on a set of points.
 * 
 * @param xlist      List of x values. (Required)
 * @param ylist      List of y values. (Required)
 * @param xnew      Determines the y value to forecast. (Required)
 * @return Returns a struct. 
 * @author James Stevenson (james.m.stevenson@gmail.com) 
 * @version 1, November 3, 2005 
 */
function forecast(xlist, ylist, Xnew) {
    var X = ListToArray(xlist);
    var Y = ListToArray(ylist);
    var i = 0;
    var n = arrayLen(X);
    var minX = 0;
    var maxX = 0;
    var minY = 0;
    var maxY = 0;
    var sumX = 0;
    var sumY = 0;
    var sumXsquared = 0;
    var sumYsquared = 0;
    var sumXY = 0;
    var Sxx = 0;
    var Syy = 0;
    var Sxy = 0;
    var b = 0;
    var a = 0;
    var SSR = 0;
    var SSE = 0;
    var residual = ArrayNew(2);
    var maxAbsoluteResidual = 0.0;
    var Ynew = 0;
    var regressionVars = ArrayNew(2);
    //test args
    if (arrayLen(X) NEQ arrayLen(Y)) 
    {
        regressionVars[1][1] = "x and y lists do not have the same number of values";
        regressionVars[2][1] = "error.";
    }
    else if (arrayLen(X) LT 3 AND arrayLen(Y) LT 3) 
    {
        
        regressionVars[1][1] = "you need at least three data points";
        regressionVars[2][1] = "error.";
    }
    else 
    { 
        for (i=1; i LT n+1; i=i+1) 
        {    
            //Find sum of squares for x,y and sum of xy
            minX = min(minX,X[i]);
            maxX = max(maxX,X[i]);
            minY = min(minY,Y[i]);
            maxY = max(maxY,Y[i]);
            sumX = sumX + X[i];        
            sumY = sumY + Y[i];        
            sumXsquared = sumXsquared + (X[i]*X[i]);    
            sumYsquared = sumYsquared + (Y[i]*Y[i]);
            sumXY = sumXY+ (X[i]*Y[i]);
        }
        //Caculate regression coefficients
        Sxx = sumXsquared-sumX*sumX/n;
        Syy = sumYsquared-sumY*sumY/n;
        Sxy = sumXY-sumX*sumY/n;
        b =Sxy/Sxx;
        a = (sumY-b*sumX)/n;
        SSR = Sxy*Sxy/Sxx;
        SSE = Syy -SSR;
        //Calculate residuals
        for (i=1; i LT n+1; i=i+1 ) 
        {           
            residual[i][1] = x[i];
            residual[i][2] = y[i]-(a+b*x[i]);
            maxAbsoluteResidual = Max(maxAbsoluteResidual, Abs(y[i]-(a+b*x[i])));
        }
        //plug Ynew valuye into standard slope-intercept form (y=mx+b) to find new data point's coordinates
        Ynew = b*Xnew+a; 
        //place all values in a 2-d array: regressionVars. Dimension 1 holds the values themselves, dimension 2 contains a descriptive label for each value
        regressionVars[1][1] = Ynew;
        regressionVars[1][2] = a;
        regressionVars[1][3] = b;
        regressionVars[1][4] = Sxx;
        regressionVars[1][5] = Syy;
        regressionVars[1][6] = Sxy;
        regressionVars[1][7] = SSR;
        regressionVars[1][8] = SSE;
        regressionVars[1][9] = SSE/(n-2);
        regressionVars[1][10] = Sxy/Sqr(Sxx*Syy);
        regressionVars[1][11] = maxAbsoluteResidual;
        regressionVars[1][12] = residual;
        regressionVars[2][1] = "new Y value, given X";
        regressionVars[2][2] = "intercept";
        regressionVars[2][3] = "slope";
        regressionVars[2][4] = "Sxx (Sum of X Products)";
        regressionVars[2][5] = "Syy (Sum of Y products)";
        regressionVars[2][6] = "Sxy (Sum X & Y Products)";
        regressionVars[2][7] = "SSR (Sum of Squared Residuals)";
        regressionVars[2][8] = "SSE (Sum of Squared Errors)";
        regressionVars[2][9] = "MSE (Mean Squared Error)";
        regressionVars[2][10] = "Pearson Residual"; // raw residual (y-m), scaled by the estimated standard deviation of y.
        regressionVars[2][11] = "Max Absolute Residual";
        regressionVars[2][12] = "residuals for given data points"; //this value is a 2-d array
    }
    return regressionVars;
}