What is the regression equation based on the following?: {(1,2),(2,3),(4,2),(5,6),(8,7)}

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Answer 1 · 2016-06-27T09:21:43

#y=(-19/15)x+136/15#

The fit for given data is of the type #y=mx+c#, where

#m=(nSigmaxy-(Sigmax)(Sigmay))/(nSigmax^2-(Sigmax)^2)# and #c=(Sigmay-mSigmax)/n#

In the data set #{(1,2),(2,3),(4,2),(5,6),(8,7)}#, we have #n=5#,

#Sigmax=1+2+4+5+8=20#, #Sigmay=2+3+2+6+7=20#,

#Sigmaxy=1*2+2*3+4*2+5*6+8*7=2+6+8+30+56=102#

#Sigmax^2=1^2+2^2+4^2+5^2+8^2=1+4+16+25+64=110# and

#Sigmay^2=2^2+3^2+2^2+6^2+7^2=4+9+4+36+49=102#

Hence #m=(5*102-20*20)/(5*110-20^2)=-190/150=-19/15#

and #c=(20-(-19/15)*20)/5=(20+380/15)/5=4+380/75=4+76/15=136/15#

Hence, regression equation is #y=(-19/15)x+136/15#