Polynomial

# Polynomial - ∑ ∑ = = = j x y x a M i j i i M i k j i n k k ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ = = = = = = = = = = = =

This preview shows pages 1–5. Sign up to view the full content.

Regression and Correlation of Data Objective: Fit a polynomial with the Least Squares Method

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Fitting the polynomial with the least squares approach Regression and Correlation of Data n x a x a x a a x P n n + + + + = ... ) ( 2 2 1 0 Least squares method can also be sued to determine the coefficients: n ,...,a , a , a a 2 1 0 2 1 1 2 )] ( [ = = - = = n i i n i n i i x P y e SSE 0 ) ( = SSE a i i = 0, 1, 2, …, n (n+1 equations) (n+1 coefficients)
Regression and Correlation of Data In this case, we wish to minimize: where: M is the number of data points minus 1 The minimization step leads to a system of n +1 normal equations in n +1 unknowns. The unknowns are the coefficients of the polynomial a 0 , a 1 , a 2 , … , a n ( 29 2 0 ) ( P = - M i i i x y

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
n. ..., 1, , 0 where , 0 0 0 = =
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ∑ ∑ = = + = j x y x a M i j i i M i k j i n k k ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ = = = = + + = = = + = = = = = = = = = + + + + = + + + + = + + + + M i M i n i i n i n M i M i n i n i M i n i M i M i i i n i n M i M i i i M i i M i M i i i n i n M i M i i i M i i x y x a x a x a x a x y x a x a x a x a x y x a x a x a x a 2 2 2 1 1 1 1 3 2 2 1 1 2 2 1 1 ... , ... , ... Regression and Correlation of Data • Gives a system of equations simultaneous equations that can be solved. Example 45...
View Full Document

## This note was uploaded on 02/13/2012 for the course MATH 2320 taught by Professor Glyn during the Fall '11 term at Minnesota.

### Page1 / 5

Polynomial - ∑ ∑ = = = j x y x a M i j i i M i k j i n k k ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ = = = = = = = = = = = =

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online