Working data will be in C:\Program Files\sp2000\users\default\_Data > ?qchisq > A_matrix(c(1,-7/25,0,24/25),2,2) > A [,1] [,2] [1,] 1.00 0.00 [2,] -0.28 0.96 > A %*% t(A) [,1] [,2] [1,] 1.00 -0.28 [2,] -0.28 1.00 > z_matrix(rnorm(200),100,2) > x_A %*% t(z) > plot(x) Error in plot: Lengths of x and y m ust match > x_t(x) > plot(x) > xbar_apply(x,2,mean) > xbar [1] -0.02117131521140350 -0.08574032939264949 > Sn_var(x) > Sn [,1] [,2] [1,] 1.0829109703422160 -0.2836839909334069 [2,] -0.2836839909334069 1.1685965069551480 > ?svd > svS_svd(Sn) > svS $d: [1] 1.4126546091737940 0.8388528681235701 $v: [,1] [,2] [1,] -0.6521773084844609 0.7580664603436591 [2,] 0.7580664603436591 0.6521773084844609 $u: [,1] [,2] [1,] -0.6521773084844609 0.7580664603436591 [2,] 0.7580664603436589 0.6521773084844608 > B_t(svS$v %*% (t(svS$u) * sqrt(svS$d))) > B %*% B [,1] [,2] [1,] 1.0829109703422160 -0.283683990933407 [2,] -0.2836839909334072 1.168596506955148 > Sn [,1] [,2] [1,] 1.0829109703422160 -0.2836839909334069 [2,] -0.2836839909334069 1.1685965069551480 > rsq_qchisq(.90,1)/100 > pi [1] 0.2990794408455506 0.1990555744971020 0.2042072962836686 [4] 0.2976576883736788 > Pi [1] 3.141592653589793 > theta_seq(0,2*Pi,len=200) > v=sqrt(rsq)*rbind(cos(theta),sin(theta)) Error in parse(text = txt): Syntax error: "=" used illegally at this p oint: v= > v_sqrt(rsq)*rbind(cos(theta),sin(theta)) > dim(v) [1] 2 200 > v_sqrt(rsq)*cbind(cos(theta),sin(theta)) > dim(v) [1] 200 2 > lines(v) > xbar [1] -0.02117131521140350 -0.08574032939264949 > xbarM_matrix(xbar,200,2,byrow=T) > xbarM [,1] [,2] [1,] -0.0211713152114035 -0.08574032939264949 [2,] -0.0211713152114035 -0.08574032939264949 [3,] -0.0211713152114035 -0.08574032939264949 [4,] -0.0211713152114035 -0.08574032939264949 [5,] -0.0211713152114035 -0.08574032939264949 [6,] -0.0211713152114035 -0.08574032939264949 [7,] -0.0211713152114035 -0.08574032939264949 [8,] -0.0211713152114035 -0.08574032939264949 [9,] -0.0211713152114035 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-0.0211713152114035 -0.08574032939264949 [177,] -0.0211713152114035 -0.08574032939264949 [178,] -0.0211713152114035 -0.08574032939264949 [179,] -0.0211713152114035 -0.08574032939264949 [180,] -0.0211713152114035 -0.08574032939264949 [181,] -0.0211713152114035 -0.08574032939264949 [182,] -0.0211713152114035 -0.08574032939264949 [183,] -0.0211713152114035 -0.08574032939264949 [184,] -0.0211713152114035 -0.08574032939264949 [185,] -0.0211713152114035 -0.08574032939264949 [186,] -0.0211713152114035 -0.08574032939264949 [187,] -0.0211713152114035 -0.08574032939264949 [188,] -0.0211713152114035 -0.08574032939264949 [189,] -0.0211713152114035 -0.08574032939264949 [190,] -0.0211713152114035 -0.08574032939264949 [191,] -0.0211713152114035 -0.08574032939264949 [192,] -0.0211713152114035 -0.08574032939264949 [193,] -0.0211713152114035 -0.08574032939264949 [194,] -0.0211713152114035 -0.08574032939264949 [195,] -0.0211713152114035 -0.08574032939264949 [196,] -0.0211713152114035 -0.08574032939264949 [197,] -0.0211713152114035 -0.08574032939264949 [198,] -0.0211713152114035 -0.08574032939264949 [199,] -0.0211713152114035 -0.08574032939264949 [200,] -0.0211713152114035 -0.08574032939264949 > plot(x) > lines(xbarM+v %*% t(B)) > rsq_qchisq(.90,2)/100 > v_sqrt(rsq)*cbind(cos(theta),sin(theta)) > plot(x) > lines(xbarM+v %*% t(B)) >