Least Squares, Medians, and the Indy 500 in Java

Generator QR Code 2d barcode in Java Least Squares, Medians, and the Indy 500
13
QR Code Decoder In Java
Using Barcode Control SDK for Java Control to generate, create, read, scan barcode image in Java applications.
Least Squares, Medians, and the Indy 500
Denso QR Bar Code Encoder In Java
Using Barcode encoder for Java Control to generate, create QR Code image in Java applications.
Figure 138 shows the situation in general We have taken the baseline along the x-axis, with the leftmost vertex of the triangle at the point (0, 0) This simpli es the calculations greatly and does not limit the generality of our arguments
Recognize QR-Code In Java
Using Barcode recognizer for Java Control to read, scan read, scan image in Java applications.
(x2,y2)
Bar Code Encoder In Java
Using Barcode creation for Java Control to generate, create bar code image in Java applications.
m3 -- -- -- -- -- -> (x2/2,y2/2) ((x1+x2)/2,y2/2)
Bar Code Scanner In Java
Using Barcode scanner for Java Control to read, scan read, scan image in Java applications.
m1-- ->
Painting QR Code In C#.NET
Using Barcode encoder for .NET framework Control to generate, create QR image in .NET framework applications.
m2-- -- > (x1,0)
QR Code Printer In VS .NET
Using Barcode encoder for ASP.NET Control to generate, create QR Code ISO/IEC18004 image in ASP.NET applications.
(0,0)
Create Quick Response Code In Visual Studio .NET
Using Barcode generator for Visual Studio .NET Control to generate, create QR Code image in Visual Studio .NET applications.
First the point (x, y) is the point ((x1 + x2 )/3, (y2 /3)), so the point (x, y) is 1/3 of the distance from the baseline toward the vertex, P2 Now we must show that the medians meet at that point The equations of the three medians shown are as follows: m1: m2: m3: y2 x x1 + x 2 x 1 y2 y2 y= + x x1 2x2 x2 2x1 y= y= x 1 y2 2y2 + x 2x2 x1 2x2 x1
QR Code ISO/IEC18004 Printer In Visual Basic .NET
Using Barcode creation for .NET Control to generate, create Quick Response Code image in .NET applications.
It is easy to verify that the point ((x1 + x2 )/3, (y2 /3)) lies on each of the lines and hence is the point of intersection of these median lines
Code 128C Creator In Java
Using Barcode printer for Java Control to generate, create Code-128 image in Java applications.
The Median Median Line
Draw Code 39 Full ASCII In Java
Using Barcode creator for Java Control to generate, create USS Code 39 image in Java applications.
These facts suggest two ways to determine the equation of the median median line They are as follows: 1 First, determine the slope of the line joining P1 and P3 This is the slope of the median median line Second, determine the point (x, y) Finally, nd the median median line using the slope and a point on the line 2 Determine the slope of the line joining P1 and P3 Then determine the equations of two of the medians and solve them simultaneously to determine the point of intersection The median median line can be found using the slope and a point on the line To these two methods, suggested by the facts above, we add a third method 3 Determine the intercept of the line joining P1 and P3 and the intercept of the line through P2 with the slope of the line through P1 and P3 The intercept of the median median line is the average of twice the rst intercept plus the second intercept (and its slope is the slope of the line joining P1 and P3 ) Method 1 is by far the easiest of the three methods although all are valid Methods 2 and 3 are probably useful only if one wants to practice nding equations of lines and doing some algebra! Method 2 is simply doing the proof above with actual data We will not prove that method 3 is valid but the proof is fairly easy
Painting Barcode In Java
Using Barcode generator for Java Control to generate, create barcode image in Java applications.
When Are the Lines Identical
ITF-14 Encoder In Java
Using Barcode printer for Java Control to generate, create EAN - 14 image in Java applications.
It turns out that if x2 = x, then the least squares line and the median median line are identical To show this, consider the diagram in Figure 139 where we have taken the base of the triangle along the x-axis and the vertex of the triangle at (x1 /2, y2 ) since 0 + x1 + 3 x1 2 = x1 2
Paint Code 39 Full ASCII In VB.NET
Using Barcode maker for Visual Studio .NET Control to generate, create Code 39 Extended image in .NET applications.
(x1/2,y2)
ECC200 Creator In VS .NET
Using Barcode maker for ASP.NET Control to generate, create Data Matrix ECC200 image in ASP.NET applications.
(x1/2,y2/3)
Code 39 Full ASCII Scanner In .NET
Using Barcode recognizer for Visual Studio .NET Control to read, scan read, scan image in .NET framework applications.
(0,0)
Bar Code Generation In .NET
Using Barcode generation for Visual Studio .NET Control to generate, create bar code image in .NET framework applications.
(x1,0)
Print EAN13 In .NET Framework
Using Barcode generation for Visual Studio .NET Control to generate, create EAN13 image in VS .NET applications.
13
Encoding UPC Code In Visual Studio .NET
Using Barcode creator for Visual Studio .NET Control to generate, create UPC-A Supplement 5 image in .NET framework applications.
Least Squares, Medians, and the Indy 500
Recognizing Barcode In .NET
Using Barcode scanner for .NET framework Control to read, scan read, scan image in .NET framework applications.
Now = Here
n n i=1 (xi x)(yi y) n 2 i=1 (xi x)
(xi x)(yi y) = 0
x1 2 x1 2
y2 x1 x1 + 3 2 2 y2 3 =0
y2
y2 3
+ x1
so = 0 Also, = y x = y = y2 /3 So the least squares line is y = y2 /3 But this is also the median median line since the median median line passes through (x, y) and has slope 0 It is not frequent that x2 = x, but if these values are close, we expect the least squares line and the median median line to also be close We now proceed to an example using the Indianapolis 500-mile race winning speeds The reason for using these speeds as an example is that the data are divided naturally into three parts due to the fact that the race was not held during World War I (1917 and 1918) and World War II (1942 1946) We admit that the three periods of data are far from equal in size The data have been given above by year; we now show the median points for each of the three time periods (Table 137 and Figure 1310)
Table 137 Period 1911 1916 1919 1941 1947 2008 Median (years) 19135 1930 19775 Median (speed) 8060 10045 14995