L12_Dynamic

L12_Dynamic - Plan for the Session • Questions •...

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Unformatted text preview: Plan for the Session • Questions? • Complete some random topics • Lecture on Design of Dynamic Systems (Signal / Response Systems) • Recitation on HW#5? 16.881 MIT Dummy Levels and µ • B efore • A fter – Set SP2=SP3 – µ rises – Predictions unaffected Factor Effects on the S/N Ratio 10 12 14 16 18 S P 1 S P 2 S P 3 D A 1 D A 2 D A 3 C U P 1 C U P 2 C U P 3 P P 1 P P 2 P P 3 S/N Ratio (dB) Factor Effects on the S/N Ratio 10 12 14 16 18 S P 1 S P 2 S P 3 D A 1 D A 2 D A 3 C U P 1 C U P 2 C U P 3 P P 1 P P 2 P P 3 S/N Ratio (dB) µ µ 16.881 MIT Number of Tests • One at a time – Listed as small • Orthogonal Array – Listed as small • W hite Box – Listed as medium 16.881 MIT Linear Regression • Fits a linear model to data Y i β 0 β 1 X i . ε i 16.881 MIT Error Terms • Error should be independent – Within replicates – Between X values 6 4 2 0 0 0.5 1 1.5 2 Population regression line 2 Population data points 16.881 Error terms MIT Least Squares Estimators • We want to choose values of b o and b 1 that minimize the sum squared error , SSE b 0 b 1 i 2 y i b 0 b 1 x i . • Take the derivatives, set them equal to zero and you get b 1 i x i mean x ( ) y i mean y ( ) . i x i mean x ( ) 2 b 0 mean y ( ) ( ) b 1 . mean x MIT Distribution of Error • Homoscedasticity • Heteroscedasticity 4 2 0 2 4 6 0 0.5 1 1.5 2 Population regression line Population data points Error terms 16.881 MIT Cautions Re: Regression...
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This note was uploaded on 11/08/2011 for the course AERO 16.851 taught by Professor Ldavidmiller during the Fall '03 term at MIT.

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L12_Dynamic - Plan for the Session • Questions •...

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