13 Regression - Linear Regression Application to Pacific...

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Linear Regression Application to Pacific Halibut Lec13.Regression1.ssc D&B Chp 12, Sections 1,2,3,4 & 6 Skip logistic discussion
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Pacific halibut (Hippoglosus stenolepis) z Largest of the flatfish z Up to 2.5m in length z Up to 500 lbs in wt z Fishery landings of 98 million pounds z $2.25 per pound ex- vessel price
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Population Range
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Halibut Longliners
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Catch Per Unit Effort z CPUE z Pounds per skate z Biomass z Millions of pounds
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halibut = read.table("halibut.txt" header=T) halibut cpue biomass 1 132 171.19 2 143 179.71 3 160 182.77 4 171 190.01 5 145 199.12 6 155 208.18 7 178 214.28 8 179 222.83 9 177 239.13 . . . attach(halibut) plot(biomass cpue)
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biomass 150 200 250 300 150 200 250 cpue
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x 02468 1 0 01 0 2 3 4 Linear Model Slope Intercept
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) , 0 ( ~ 2 1 0 1 0 σε β ε N where Slope Intercept x y i i i i = = + + = Linear Model
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biomass 150 200 250 300 150 200 250 cpue 4 . 0 100 1 0 1 0 = = + + = β ε i i i x y
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biomass 150 200 250 300 150 200 250 cpue 0 . 1 0 . 0 1 0 1 0 = = + + = β ε i i i x y
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biomass 150 200 250 300 150 200 250 cpue 0 . 1 0 . 0 1 0 1 0 = = + + = β ε i i i x y
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biomass 150 200 250 300 - 4 0 2 04 06 res id ua ls
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Regression Procedure z Assuming a linear model z Find the best estimates of β 0 and β 1 z Using the criteria: () i i n i i i obs x y y y 1 0 1 2 where minimize ββ + = =
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biomass 150 200 250 300 150 200 250 cpue B1 = 0.8 B1 = 0.6 B1 = 0.4
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biomass 150 200 250 300 150 200 250 cpue y = 66.3 + 0.57 x
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Examine Effect of Change in Parameter on SSE my.SSE = function(b0, b1, data = halibut) { y = data[ 1] x = data[ 2] return( sum((y - b0 - b1 * x)^2) ) } my.SSE(66.3, 0.57 ) 41999.9 my.SSE(66.3, 0.4 ) 141333.5 my.SSE(66.3, 0.8 ) 211377.7
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This note was uploaded on 11/12/2009 for the course BTRY 3010 at Cornell University (Engineering School).

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13 Regression - Linear Regression Application to Pacific...

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