Youcanfitthequadraticequation E(Y ) = 0+1x+2x2 byfittingamultipleregressionmodel with x1 = x and x2 = x2. (a) Simulate100independentobservationsfromthemodel Y

Youcanfitthequadraticequation E(Y ) = β0+β1x+β2x2 byfittingamultipleregressionmodel with x1 = x and x2 = x2.

(a) Simulate100independentobservationsfromthemodel Y = 40.0−5.0x+0.5x2+ϵ, where X has auniformdistributionover[0,10]and ϵ ∼ N(0, 1). Plotthedataandfitthequadratic model.Reporthowthefittedequationcompareswiththetruerelationship.

(b) Findthecorrelationbetween x and y and explainwhyitissoweakeventhoughtheplot showsastrongrelationshipwithalarge R2 valueforthequadraticmodel.