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barcode font reporting services Regression in Software
Regression QRCode Reader In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. QR Code 2d Barcode Generator In None Using Barcode generator for Software Control to generate, create QR Code image in Software applications. One of the main purposes of curve fitting is to estimate one of the variables (the dependent variable) from the other (the independent variable). The process of estimation is often referred to as regression. If y is to be estimated from x by means of some equation, we call the equation a regression equation of y on x and the corresponding curve a regression curve of y on x. Read QR In None Using Barcode reader for Software Control to read, scan read, scan image in Software applications. QR Code JIS X 0510 Creator In Visual C# Using Barcode drawer for Visual Studio .NET Control to generate, create Denso QR Bar Code image in .NET framework applications. CHAPTER 8 Curve Fitting, Regression, and Correlation
QR Generation In .NET Using Barcode creation for ASP.NET Control to generate, create QR Code image in ASP.NET applications. Generate Quick Response Code In Visual Studio .NET Using Barcode creation for .NET Control to generate, create Quick Response Code image in Visual Studio .NET applications. Fig. 81 Make QR Code ISO/IEC18004 In Visual Basic .NET Using Barcode maker for .NET framework Control to generate, create QR Code image in Visual Studio .NET applications. Barcode Creator In None Using Barcode encoder for Software Control to generate, create bar code image in Software applications. Fig. 82 USS Code 128 Drawer In None Using Barcode maker for Software Control to generate, create Code 128 Code Set A image in Software applications. Encode Barcode In None Using Barcode creation for Software Control to generate, create bar code image in Software applications. Fig. 83 Data Matrix 2d Barcode Generator In None Using Barcode printer for Software Control to generate, create Data Matrix image in Software applications. Making Code 39 Extended In None Using Barcode generation for Software Control to generate, create Code 3/9 image in Software applications. The Method of Least Squares
Encode Postnet In None Using Barcode generation for Software Control to generate, create USPS POSTal Numeric Encoding Technique Barcode image in Software applications. Making Data Matrix 2d Barcode In ObjectiveC Using Barcode creator for iPad Control to generate, create Data Matrix image in iPad applications. Generally, more than one curve of a given type will appear to fit a set of data. To avoid individual judgment in constructing lines, parabolas, or other approximating curves, it is necessary to agree on a definition of a bestfitting line, bestfitting parabola, etc. To motivate a possible definition, consider Fig. 84 in which the data points are (x1, y1), . . . , (xn, yn). For a given value of x, say, x1, there will be a difference between the value y1 and the corresponding value as determined from the curve C. We denote this difference by d1, which is sometimes referred to as a deviation, error, or residual and may be positive, negative, or zero. Similarly, corresponding to the values x2, . . . , xn, we obtain the deviations d2, . . . , dn. UPC  13 Reader In None Using Barcode reader for Software Control to read, scan read, scan image in Software applications. Decoding Code 3/9 In VB.NET Using Barcode reader for .NET Control to read, scan read, scan image in .NET framework applications. Fig. 84 Recognizing Barcode In Java Using Barcode scanner for Java Control to read, scan read, scan image in Java applications. Matrix Barcode Drawer In VS .NET Using Barcode creation for Visual Studio .NET Control to generate, create Matrix Barcode image in VS .NET applications. A measure of the goodness of fit of the curve C to the set of data is provided by the quantity d 2 d 2 c d 2. If this is small, the fit is good, if it is large, the fit is bad. We therefore make the follow1 2 n ing definition. Definition Of all curves in a given family of curves approximating a set of n data points, a curve having the property that d2 1 d2 2 c d2 n a minimum Code 128 Code Set B Maker In ObjectiveC Using Barcode maker for iPhone Control to generate, create Code128 image in iPhone applications. Create ECC200 In None Using Barcode printer for Online Control to generate, create Data Matrix image in Online applications. is called a bestfitting curve in the family. A curve having this property is said to fit the data in the leastsquares sense and is called a leastsquares regression curve, or simply a leastsquares curve. A line having this property is called a leastsquares line; a parabola with this property is called a leastsquares parabola, etc. It is customary to employ the above definition when x is the independent variable and y is the dependent variable. If x is the dependent variable, the definition is modified by considering horizontal instead of vertical deviations, which amounts to interchanging the x and y axes. These two definitions lead in general to two different leastsquares curves. Unless otherwise specified, we shall consider y as the dependent and x as the independent variable. CHAPTER 8 Curve Fitting, Regression, and Correlation
It is possible to define another leastsquares curve by considering perpendicular distances from the data points to the curve instead of either vertical or horizontal distances. However, this is not used very often. The LeastSquares Line
By using the above definition, we can show (see Problem 8.3) that the leastsquares line approximating the set of points (x1, y1), . . . , (xn, yn) has the equation y a bx (3) where the constants a and b are determined by solving simultaneously the equations ay a xy an a ax b ax b a x2 (4) which are called the normal equations for the leastsquares line. Note that we have for brevity used gy, gxy instead of g n 1 yj, g n 1xj yj. The normal equations (4) are easily remembered by observing that the first equation j j can be obtained formally by summing on both sides of (3), while the second equation is obtained formally by first multiplying both sides of (3) by x and then summing. Of course, this is not a derivation of the normal equations but only a means for remembering them. The values of a and b obtained from (4) are given by Q a yR Q a x2 R a n a x2 The result for b in (5) can also be written b Here, as usual, a bar indicates mean, e.g., x # by n yields a (x a (x x)( y # x)2 # y) # (6) Q a xR Q a xyR Q a xR

