The Correlation Coefficient in Java
The Correlation Coefficient PDF 417 Recognizer In Java Using Barcode Control SDK for Java Control to generate, create, read, scan barcode image in Java applications. Print PDF 417 In Java Using Barcode printer for Java Control to generate, create PDF 417 image in Java applications. Although the regression line in Figure 81 seems to indicate an upward trend, we don t know how well this line actually fits the data. If the line and data have only a slight correlation, the regression line is of little interest. If the line fits the data well, it is of much greater value. The most common way to determine the correlation of the data to the regression line is to compute the correlation coefficient, which is a number between 1 and 1. The correlation coefficient represents the amount of deviation from the mean that is explained by the line. This may sound confusing, but it really isn t. The correlation coefficient is related to the PDF417 2d Barcode Decoder In Java Using Barcode decoder for Java Control to read, scan read, scan image in Java applications. Barcode Encoder In Java Using Barcode generation for Java Control to generate, create bar code image in Java applications. The Art of Java
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PDF417 Creator In VB.NET Using Barcode creation for VS .NET Control to generate, create PDF 417 image in .NET framework applications. Paint Bar Code In Java Using Barcode generator for Java Control to generate, create bar code image in Java applications. distance each data point is from the line. If the correlation coefficient is 1, the data corresponds perfectly to the line. A coefficient of 0 means that there is no correlation between the line and the data. (In this case, any line would be about as good!) The sign of the correlation coefficient must be set according to the sign of the slope of the regression line, which is b. If the correlation coefficient is positive, it means that there is a direct relationship between the dependent variable and the independent variable. If the correlation coefficient is negative, then an inverse relationship exists. The formula to find the correlation coefficient is Code128 Printer In Java Using Barcode encoder for Java Control to generate, create Code 128 Code Set C image in Java applications. European Article Number 13 Printer In Java Using Barcode encoder for Java Control to generate, create EAN / UCC  13 image in Java applications. where Mx is the mean of X and My is the mean of Y. The sign is set based on the sign of the slope of the regression line. Generally, an absolute value of 0.81 or greater is considered a strong correlation. It means that about 66 percent of the data fits the regression line. To convert any correlation coefficient into a percentage, simply square it. This squared value is called the coefficient of determination. The regress( ) method, shown next, computes the regression equation and the correlation coefficient: Encoding Code 9/3 In Java Using Barcode maker for Java Control to generate, create USS93 image in Java applications. Paint GTIN  13 In None Using Barcode maker for Software Control to generate, create UPC  13 image in Software applications. /* Compute the regression equation and coefficient of correlation for a set of values. The values represent the Y coordinate. The X coordinate is time (i.e., ascending increments of 1). */ Decoding Code 39 Full ASCII In VB.NET Using Barcode decoder for .NET framework Control to read, scan read, scan image in .NET framework applications. Bar Code Creator In ObjectiveC Using Barcode encoder for iPhone Control to generate, create barcode image in iPhone applications. 8: Statistics, Graphing, and Java
Generating UCC  12 In ObjectiveC Using Barcode printer for iPad Control to generate, create EAN128 image in iPad applications. Drawing Linear In VS .NET Using Barcode generator for .NET framework Control to generate, create 1D image in .NET framework applications. public static RegData regress(double[] vals) { double a, b, yAvg, xAvg, temp, temp2, cor; double vals2[] = new double[vals.length]; // Create number format with 2 decimal digits. NumberFormat nf = NumberFormat.getInstance(); nf.setMaximumFractionDigits(2); // Find mean of Y values. yAvg = mean(vals); // Find mean of X component. xAvg = 0.0; for(int i=0; i < vals.length; i++) xAvg += i; xAvg /= vals.length; // Find b. temp = temp2 = 0.0; for(int i=0; i < vals.length; i++) { temp += (vals[i]yAvg) * (ixAvg); temp2 += (ixAvg) * (ixAvg); } b = temp/temp2; // Find a. a = yAvg  (b*xAvg); // Compute the coefficient of correlation. for(int i=0; i < vals.length; i++) vals2[i] = i+1; cor = temp/vals.length; cor /= stdDev(vals) * stdDev(vals2); return new RegData(a, b, cor, "Y = " + nf.format(a) + " + " + nf.format(b) + " * X"); } } ECC200 Recognizer In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. Data Matrix 2d Barcode Reader In Java Using Barcode reader for Java Control to read, scan read, scan image in Java applications. It is important to point out that regress( ) assumes that the independent variable (X) is time that is, the stepwise progression of events represented in units of one. The mean of the X values is computed using this sequence: // Find mean of X component. xAvg = 0.0; The Art of Java
for(int i=0; i < vals.length; i++) xAvg += i; xAvg /= vals.length; Here, the values from 0 to the number of elements in the set are summed and then divided by the number of the elements. This yields the average of X. Because time is used for the X axis, regress( ) performs what is sometimes called a timeseries analysis. This is why only a single array of values need be passed. It would be possible to modify regress( ) to accept two arrays, one containing the Y values and one containing the X values, but this was not necessary for the purposes of this chapter. The regress( ) method returns the values of a and b, a string representation of the regression equation, and the correlation coefficient, contained within a RegData object. RegData is shown here: // This class holds the regression analysis data. class RegData { public double a, b; public double cor; public String equation; public RegData(double i, double j, double k, String str) { a = i; b = j; cor = k; equation = str; } }

