barcode font reporting services (a) The linear regression equation of z on x and y can be written z a bx cy in Software

Paint Quick Response Code in Software (a) The linear regression equation of z on x and y can be written z a bx cy

(a) The linear regression equation of z on x and y can be written z a bx cy
Recognizing QR Code 2d Barcode In None
Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications.
QR Code ISO/IEC18004 Creation In None
Using Barcode creation for Software Control to generate, create Quick Response Code image in Software applications.
The normal equations (21), page 269, are given by az (1) a xz a yz na a ax a ay b ax c ay c a xy c a y2
QR Code Scanner In None
Using Barcode scanner for Software Control to read, scan read, scan image in Software applications.
Make QR Code ISO/IEC18004 In Visual C#
Using Barcode encoder for .NET Control to generate, create QR Code ISO/IEC18004 image in VS .NET applications.
b a x2 b a xy
Creating QR In Visual Studio .NET
Using Barcode drawer for ASP.NET Control to generate, create QR image in ASP.NET applications.
QR Code 2d Barcode Encoder In .NET
Using Barcode generation for VS .NET Control to generate, create QR Code image in .NET applications.
The work involved in computing the sums can be arranged as in Table 8-12. Table 8-12
QR Code JIS X 0510 Generator In Visual Basic .NET
Using Barcode generator for VS .NET Control to generate, create QR Code image in .NET applications.
Making EAN13 In None
Using Barcode drawer for Software Control to generate, create EAN-13 image in Software applications.
z 64 71 53 67 55 58 77 57 56 51 76 68 gz 753
Barcode Drawer In None
Using Barcode creation for Software Control to generate, create barcode image in Software applications.
Making Data Matrix In None
Using Barcode maker for Software Control to generate, create Data Matrix image in Software applications.
x 57 59 49 62 51 50 55 48 52 42 61 57 gx 643
GS1 128 Generator In None
Using Barcode encoder for Software Control to generate, create USS-128 image in Software applications.
Generating Code-39 In None
Using Barcode encoder for Software Control to generate, create Code 3/9 image in Software applications.
y 8 10 6 11 8 7 10 9 10 6 12 9 gy 106
Making International Standard Serial Number In None
Using Barcode creation for Software Control to generate, create International Standard Serial Number image in Software applications.
Painting DataMatrix In VS .NET
Using Barcode creation for Reporting Service Control to generate, create ECC200 image in Reporting Service applications.
z2 4096 5041 2809 4489 3025 3364 5929 3249 3136 2601 5776 4624 gz2 48,139
Bar Code Printer In Java
Using Barcode encoder for Java Control to generate, create barcode image in Java applications.
Decoding USS-128 In Visual Basic .NET
Using Barcode reader for Visual Studio .NET Control to read, scan read, scan image in .NET applications.
x2 3249 3481 2401 3844 2601 2500 3025 2304 2704 1764 3721 3249 gx2 34,843
Drawing UCC-128 In Objective-C
Using Barcode drawer for iPad Control to generate, create UCC - 12 image in iPad applications.
Printing 1D Barcode In Visual Studio .NET
Using Barcode creation for VS .NET Control to generate, create 1D Barcode image in .NET framework applications.
y2 64 100 36 121 64 49 100 81 100 36 144 81 gy2 976
Generate 1D Barcode In Java
Using Barcode maker for Java Control to generate, create Linear Barcode image in Java applications.
Painting Barcode In Objective-C
Using Barcode encoder for iPhone Control to generate, create bar code image in iPhone applications.
xz 3648 4189 2597 4154 2805 2900 4235 2736 2912 2142 4636 3876 gxz 40,830
yx 512 710 318 737 440 406 770 513 560 306 912 612 gyz 6796
xy 456 590 294 682 408 350 550 432 520 252 732 513 gxy 5779
CHAPTER 8 Curve Fitting, Regression, and Correlation
Using this table, the normal equations (1) become 12a (2) 643a 106a Solving, a (3) 3.6512, b 0.8546, c z 643b 5779b 106c 5779c 976c 753 40,830 6796
34,843b
1.5063, and the required regression equation is 3.65 0.855x 1.506y
(b) Using the regression equation (3), we obtain the estimated values of z, denoted by zest, by substituting the corresponding values of x and y. The results are given in Table 8-13 together with the sample values of z. Table 8-13 zest z 64.414 69.136 54.564 73.206 59.286 56.925 65.717 58.229 63.153 48.582 73.857 65.920 64 (c) Putting x 71 53 54 and y 67 55 58 77 57 56 51 76 68
9 in (3), the estimated weight is zest
63.356, or about 63 lb.
Standard error of estimate 8.20. If the least-squares regression line of y on x is given by y mate sy.x is given by
s2 y.x a y2 a ay n
bx, prove that the standard error of esti-
b a xy
a bx. Then
The values of y as estimated from the regression line are given by yest s2 y.x a (y n a y(y a bx) yest)2 a (y a n bx)2 a n an a ax bx)
a a (y
b a x(y
a (y a x(y a
bx) bx)
ay a xy
b ax b a x2
since from the normal equations ay Then s2 y.x an a y(y n b ax a bx) a xy ay
a ax a ay n
b a x2 b a xy
This result can be extended to nonlinear regression equations.
8.21. Prove that the result in Problem 8.20 can be written s2 y.x
Method 1 Let x xr
a (y
y)2 #
b a (x n
x)(y #
y) #
x, y # ns2 y.x
yr a y2 a (yr a (yr2
y. Then from Problem 8.20 # a ay y)2 # 2yr y # b a xy a a (yr y2) # y) # aQ a yr b a (xr ny R # x)(yr # y) # xyr # xr y # x y) ##
b a (xryr
CHAPTER 8 Curve Fitting, Regression, and Correlation
2y a yr # ny2 # any # ny2 # any # bx a yr # by a xr # bnx y ##
a yr2 a yr2
b a xryr bnx y ## bx) #
b a xryr ny(y # # a
a yr a
b a xryr b a xryr y)2 #
a( y
b a (x
x)( y #
y) #
where we have used the results g xr 0, gyr 0 and y a bx (which follows on dividing both sides of # # the normal equation gy an bg x by n). This proves the required result. Method 2 We know that the regression line can be written as y y b(x # y a bx and then replacing a by zero, x by x x and y by y # Problem 8.20, the required result is obtained. x), which corresponds to starting with # y. When these replacements are made in #
8.22. Compute the standard error of estimate, sy.x, for the data of Problem 8.11.
From Problem 8.11(b) the regression line of y on x is y 35.82 0.476x. In Table 8-14 are listed the actual values of y (from Table 8-3) and the estimated values of y, denoted by yest, as obtained from the regression line. For example, corresponding to x 65, we have yest 35.82 0.476(65) 66.76.
Table 8-14 x y yest y yest 65 68 63 66 67 68 64 65 66.28 1.28 68 69 62 66 70 68 69.14 1.14 66 65 67.24 2.24 68 71 68.19 2.81 67 67 67.71 0.71 69 68 68.66 0.66 71 70 69.62 0.38
66.76 65.81 67.71 1.24 0.19 0.29
68.19 65.33 0.81 0.67
Also listed are the values y s2 y.x and sy.x !1.642 a (y n
yest, which are needed in computing sy x. yest)2 (1.24)2 (0.19) c 12 (0.38)2 1.642
1.28 inches.
8.23. (a) Construct two lines parallel to the regression line of Problem 8.11 and having vertical distance sy x from it. (b) Determine the percentage of data points falling between these two lines.
(a) The regression line y 35.82 0.476x as obtained in Problem 8.11 is shown solid in Fig. 8-11. The two parallel lines, each having vertical distance sy x 1.28 (see Problem 8.22) from it, are shown dashed in Fig. 8-11.
Fig. 8-11
Copyright © OnBarcode.com . All rights reserved.