Lecture 13_regression 2

Lecture 13_regression 2 - Experimental growth tannin Unit 1...

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Unformatted text preview: Experimental growth tannin Unit 1 12 2 10 1 3 8 2 4 11 3 5 6 4 6 7 5 7 2 6 8 3 Effects of food quality (% tannin content) on caterpillar growth y = a b x Sum of Square: SSY Sum of square: SSX Y X Calculate total variance for XY growth Mean growth Y 12 6.9 10 6.9 8 6.9 11 6.9 6 6.9 7 6.9 2 6.9 3 6.9 3 6.9 Deviation from the mean 5.1 3.1 1.1 4.1-0.9 0.1-4.9-3.9-3.9 Sum of products-73 ( Sum of Square: SSXY ) Y (Y Y) (X X)-4-3-2-1 1 2 3 4-20.44-9.33-2.22-4.11 0.11-9.78-11.67-15.56 (Y Y)(X X) Sum of Square for Y: SSY= 108.89 Sum of square for X: SSX= 60.00 Sum of products for XY: SSXY=-73.00 Slope (b)= SSXY SSX = = -1.22 Estimate Sum Square for regression SSR = b * SSXY = -1.22X(-73) =88.82-73.00 60.00 Growth=11.76-1.22 tannin Variance partition Sum of Square (SSY) = Total variance Residual SS Regression SS Total SS: SSY Analysis of Variance Table Response: growth Df Sum Sq Mean Sq F value tannin 1 88.817 88.817 30.974 Residuals 7 20.072 2.867 P=0.000846 (Coefficient of determination: R 2 ) Y X r 2 = Regression SS Total SS How strong the relationship? Y X r 2 = r Pearson correlation coefficient How strong the relationship? x Simple linear correlation and regression De pe nde nt va ria b le Y Inde pe nde nt va ria b le X Line a r de pe nde nc e o f Y o n X re g re s s io n No line a r de pe nde nc e b e twe e n Y a nd X c o rre la tio n Regression in R >dta<-read.csv("C:\\Documents and Settings\\bwyp\\Desktop\\regression.csv") > colnames(dta) [1] "growth" "tannin" > mod<-lm(growth~tannin, data=dta) > summary(mod) Regression in R...
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Lecture 13_regression 2 - Experimental growth tannin Unit 1...

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