HW1_Taiki - 1 EAS6939 HW#1 Name Taiki Matsumura UFID...

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Unformatted text preview: 1 EAS6939 HW#1 Name: Taiki Matsumura UFID: 6535-8317 Date: 1/13/2010 1. To solve the standard deviation of the 11 noise, I use the following formula, ඨ ∑ ሺN ୧ െ N ୫ ሻ ୬ ౯ ୧ୀଵ n ୷ െ 1 Where, n ୷ is number of the samples, N ୧ is the value of i-th samples of noise, and N ୫ is the mean of noise. I can obtain by the value of noise n ୷ ൌ 11, N ୫ ൌ െ0.138 Then I obtain the standard deviation of the noise, σ ୬ ൌ ૙. ૙ૢ૛૟ . It can be seen that σ ୬ is fairly closed to the specific standard deviation (=0.1). 2. For linear polynomial approximation with noise, I use following vector form ܍ ൌ ܡ െ X܊ Where yൌ ە ۖ ۖ ۖ ۖ ۔ ۖ ۖ ۖ ۖ ۓ െ0.0687 0.0955 0.2558 0.4731 0.3290 0.5473 0.5695 0.5277 0.6926 0.9035 1.0225 ۙ ۖ ۖ ۖ ۖ ۘ ۖ ۖ ۖ ۖ ۗ , X ൌ ۏ ێ ێ ێ ێ ێ ۍ 1 1 0.1 1 0.2 1 0.3 1 0.4 1 0.5 1 0.6 1 0.7 1 0.8 1 0.9 1 1 ے ۑ ۑ ۑ ۑ ۑ ې , ܊ ൌ ൜ b ଴ b ଵ ൠ So that I can obtain X T X ൌ ቂ 11 5.5 5.5 3.85 ቃ , X T ܡ ൌ ቄ 5.3478 3.7087 ቅ Now I write the normal equation, X T X܊ ൌ X T ܡ , 11b ଴ ൅ 5.5b ଵ ൌ 5.3478 5.5b ଴ ൅ 3.85b ଵ ൌ 3.7087 And solve it to obtain b ଴ ൌ 0.0158 and b ଵ ൌ 0.9407 . So that the least-square fit is y ො ൌ 0.0158 ൅ 0.9407x Sum of the squares of the error is calculated as SS ୣ ൌ ܍ ୰ T ܍ ܚ ൌ ܡ ܂ ܡ െ ܊ ܂ X T ܡ ൌ 3.6552 െ 3.5733 ൌ 0.0819 2 Finally related error measures, such as rms error e ୰୫ୱ , standard deviation σෝ , coefficient of multiple determination R ଶ , adjusted coefficient of multiple determination R ୟ ଶ , PRESS rms error e PrESS , and rms error by calculated analytically (by exact integration) e ୰୫ୱ_୧୬୲ are calculated as followings....
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This note was uploaded on 06/06/2011 for the course EAS 4240 taught by Professor Peterifju during the Spring '08 term at University of Florida.

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HW1_Taiki - 1 EAS6939 HW#1 Name Taiki Matsumura UFID...

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