For the 2 problems below, find the following Compute SSE, SST, and SSR using bot

Question

For the 2 problems below, find the following Compute SSE, SST, and SSR using both Definitional and Computing formula. Compute the coefficient of determination r (The same as R- ). Comment on the a. b- c. d. e. goodness of fit (That is, what does the value of r tell you about the goodness of the fit). Explain why Compute the sample correlation coefficient Determine if the slope is significant at Alpha = 0.05 Calculate F Statistics and Determine if it is Significant Problem 1. Data 14 Problem 2. Data 17 5 6 9 12 4 6

Explanation / Answer

here we fit the regression equation y=a+bx =0.2+2.6x and

here n=5 ( number of observation and p=2 ( number of regression coefficent)

a=(sum(y)*sum(x2)-sum(x)*sum(xy))/(n*sum(x2)-(sum(x))2)=(40*55-15*146)/(5*55-15*15)=0.2

b=(n*sum(xy)-sum(x)*sum(y))/ (n*sum(x2)-(sum(x))2) =(5*146-15*40)/(5*55-15*15)=2.6

(a) SST=sum(y-y-)2=80, SSE=sum(y-yest)2=1245, SSR=SST-SSE=80-12.4=67.6

(b) r2=SSR/SST=67.6/80=0.845, it is good fit as 84.5% variation is explained by the mode

(c) r=sqrt(r2)=sqrt(0.845)=0.9192

(d) for significance of slope we use t-test and t=b/SE(b)=2.6/0.6429=4.04 is more than critical t(0.05,3)=3.18 ,

so it is significant

(e) F=(SSR/(p-1))/(SSE/(n-p)) =(67.6/(2-1)/(12.4/(5-2))=16.35 is more than critical F(0.05, 1,3)=10.12, so it is significant

SE(b)=(Se/sqrt(Sxx))=2.0331/sqrt(10)=0.6429

Se=sqrt(SSE/(n-2))=sqrt(12.4/3)=2.0331

x y yest e=y-yest e2 y-y- (y-y-)2 x2 y2 xy x-x- (x-x-)2 1 3 2.8 0.2 0.04 -5 25 1 9 3 -2 4 2 7 5.4 1.6 2.56 -1 1 4 49 14 -1 1 3 5 8 -3 9 -3 9 9 25 15 0 0 4 11 10.6 0.4 0.16 3 9 16 121 44 1 1 5 14 13.2 0.8 0.64 6 36 25 196 70 2 4 sum 15 40 40 0 12.4 0 80 55 400 146 0 10

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