The table below represents minimum values of the qualities indicated, as given in a particular industry specification ASTM A53 6-70 to which ductile iron is manufactured. X X2 Y N 120 90 3 100 70 6 80 55 12 65 45 18 60 40 Here, three tensile properties of ductile cast iron are: X 1 = percentage elongation, X2 = tensile strength, kg/in?, Y = yield strength, kg/in?. Q3.1 2 Points Use RStudio to construct Y as the (5 x 1) vector of sales observations (Y); X as the (5 x 3) matrix of the predictor variables. Q3.2 9 Points In RStudio, use matrix representation and report the following: 1) (X'X)-matrix. II) (X'Y) matrix. III) b = (X'X)-4(X'Y) matrix. IV) Calculate the entries (A, B, and C) of the analysis of variance table as given below: Source df SS MS SS (b1,b2 1 bo) N A Residual n-3 B $2 = B 1-3 -C Total n-1 YOY-ny V) Construct an estimated variance-covariance matrix V(b)(=MS(Res) * (XT X)-1) and report the standard errors of the regression coefficients including intercept (up to three decimal places). [Hint: If you are using s2 value via a variable from the previous part in RStudio to construct the variance-covariance matrix then kindly convert it into numeric before using.] The table below represents minimum values of the qualities indicated, as given in a particular industry specification ASTM A53 6-70 to which ductile iron is manufactured. X X2 Y N 120 90 3 100 70 6 80 55 12 65 45 18 60 40 Here, three tensile properties of ductile cast iron are: X 1 = percentage elongation, X2 = tensile strength, kg/in?, Y = yield strength, kg/in?. Q3.1 2 Points Use RStudio to construct Y as the (5 x 1) vector of sales observations (Y); X as the (5 x 3) matrix of the predictor variables. Q3.2 9 Points In RStudio, use matrix representation and report the following: 1) (X'X)-matrix. II) (X'Y) matrix. III) b = (X'X)-4(X'Y) matrix. IV) Calculate the entries (A, B, and C) of the analysis of variance table as given below: Source df SS MS SS (b1,b2 1 bo) N A Residual n-3 B $2 = B 1-3 -C Total n-1 YOY-ny V) Construct an estimated variance-covariance matrix V(b)(=MS(Res) * (XT X)-1) and report the standard errors of the regression coefficients including intercept (up to three decimal places). [Hint: If you are using s2 value via a variable from the previous part in RStudio to construct the variance-covariance matrix then kindly convert it into numeric before using.]