ple: Given the data shown, determine the best fit ( do and a) to use in f(x) = ao + a jx. Given data Substituting the numbers into Eqs. (a) and (b): i y i 4.9 X ¡Y i 1 1 4.9 2 11.2 33.6 na, +a, >x, = Ey, 54.8 3 4 13.7 16 4 6. 20.1 36 120.6 x =Ex,y, 49.9 Σ 14 62 213.9 x, +a, 4 a, +14a, = 49.9 14a, + 62a, = 213.9 %3D Solving for ao and a, : a, = 1.908 a, = 3.019 y = 1.908 +3.019 x Example 2: Let us go back to the example seen before, namely, Total 1 3 4 6. 7 8 9. 10 y 2.3 2.1 3.6 6.8 6.9 4.9 7.5 5.8 7.5 11.8 x, xy Fit the best line in the least square sense, and draw that line in the graph paper provided (nEx,y, -ExE».) a, = na, +a, a, 2x, +a, E X = a, = i=1 i=1
ple: Given the data shown, determine the best fit ( do and a) to use in f(x) = ao + a jx. Given data Substituting the numbers into Eqs. (a) and (b): i y i 4.9 X ¡Y i 1 1 4.9 2 11.2 33.6 na, +a, >x, = Ey, 54.8 3 4 13.7 16 4 6. 20.1 36 120.6 x =Ex,y, 49.9 Σ 14 62 213.9 x, +a, 4 a, +14a, = 49.9 14a, + 62a, = 213.9 %3D Solving for ao and a, : a, = 1.908 a, = 3.019 y = 1.908 +3.019 x Example 2: Let us go back to the example seen before, namely, Total 1 3 4 6. 7 8 9. 10 y 2.3 2.1 3.6 6.8 6.9 4.9 7.5 5.8 7.5 11.8 x, xy Fit the best line in the least square sense, and draw that line in the graph paper provided (nEx,y, -ExE».) a, = na, +a, a, 2x, +a, E X = a, = i=1 i=1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
please solve Example 2.
Transcribed Image Text:Example: Given the data shown, determine the best fit ( a, and a,) to use in
f(x) = ao + a jX .
Given data
i
Substituting the numbers into Eqs.
(a) and (b):
X ¡Y i
1
1
4.9
1
4.9
11.2
9.
33.6
па, +а,
X, =
4.
13.7
16
54.8
i=1
4
20.1
36
120.6
Ex, +a,Ex}
49.9
Σ
14
62
213.9
i=1
i=1
i=1
4а, +14а, 3 49.9
14a, + 62a, = 213.9
%3D
Solving for a, and a¡ :
a, = 3.019
y = 1.908 +3.019 x
a, =1.908
Exarmple 2:
Let us go back to the example seen before, namely,
Total
1
2
3
4
6.
8
10
y
2.3
2.1
3.6
6.8
6.9
4.9
7.5
5.8
7.5
11.8
ху,
Fit the best line in the least square sense, and draw that line in the
graph paper provided
na, +a,
X; = Ly;
а, %3
i=1
a, Ex, +a, £x} =
а,
i=1
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