Program Development (2)

𝜏𝜌

Review SWEEP Operator

SWEEP Algorithm:

• D = akk

• Divide kth row using D

• For every i k rows, do:

1.B = aik

2.ith row minus using B* kth row

3.aik = -B/D

• akk = 1/D

Review SWEEP

• To use the SWEEP function for regression, suppose the matrix A contains 𝑋′𝑋 𝑋′𝑌𝑌′𝑋 𝑌′𝑌

• where X'X is k ×k. Then B = SWEEP(A,1 ... k) contains

𝑋′𝑋 −1 𝑋′𝑋 −1𝑋′𝑌

−𝑌′𝑋 𝑋′𝑋 −1 𝑌′(𝐼 − 𝑋 𝑋′𝑋 −1𝑋′)𝑌

• The partitions of B form the beta values, SSE, and a matrix proportional to the covariance of the beta values for the least-squares estimates of B in the linear model

Review SWEEP

6120

12280

006

' XX

4

6

14

y'X 42y'y

y'yX'y

y'XX'XA

Step Model1 y=b0+ b1X1

2 y=b0+b1X1+b2X2

3 y=b0+b2X2

4 y=b0

Review SWEEP

proc iml;reset print;a1={6 0 0,0 28 -12,0 -12 6};a2={14, 6, -4};a3=42;a4=a1//a2`;a5=a2//a3;A=a4||a5;

B=SWEEP(A,{1 2 3});C=SWEEP(B,{3});D=SWEEP(A,{1 2});E=SWEEP(B,{2});F=SWEEP(A,{1 3});

x1=A[{1 2},{1 2}];b=a2[{1 2},];beta=inv(x1)*b;D=SWEEP(A,{1 2});

x2=A[{1 3},{1 3}];b2=a2[{1 3},];beta2=inv(x2)*b2;E=SWEEP(A,{1 3});

Module Programming

• Create a module for regression analysis (fullstatement)

proc iml;reset print;start regg(x,y);nc=ncol(x);nb=nrow(x);satu=J(nb,1,1);xb=satu||x;beta=inv(xb`*xb)*(xb`*y);yduga = xb*beta; sisaan =y-yduga;JKR= y`*(xb*inv(xb`*xb)*xb`)*y-(y`*satu*satu`*y)/nb;JKT= y`*y-(y`*satu*satu`*y)/nb;JKG= JKT-JKR;

KTR=JKR/nc;KTG=JKG/(nb-nc-1);Fh=KTR/KTG;P_value=1-PROBF(Fh,nc,(nb-nc-1));

W=inv(xb`*xb);D=diag(W);Z=sqrt(W[1,1]);

do i=1 to (nc);Z=Z||sqrt(W[i+1,i+1]);end;SE=Z`*sqrt(KTG);

T=beta[1]/SE[1];do i=1 to (nc);T=T||(beta[i+1]/SE[i+1]);end;T_hitung=T`;

pT=1-PROBT(T_hitung[1],(nb-nc-1));do i=1 to (nc);pT=pT||(1-PROBT(T_hitung[i+1],(nb-nc-1)));end;P_value2=pT`;

F_h=Fh//.//.;p_v=P_value//.//.;hasil=beta||SE||T_hitung||P_value2||F_h||p_v;ket={beta,SE,T,P_valueT,F,P_valueF};print hasil[colname=ket];

return(hasil);finish;

A={69.0 1.0 112.5,62.8 1.0 102.5,59.8 1.0 84.5,59.0 2.0 99.5,56.3 2.0 77.0,64.8 2.0 128.0,66.5 3.0 112.0,56.5 3.0 84.0,63.5 3.0 102.5,62.5 4.0 112.5,51.3 4.0 50.5,66.5 4.0 112.0};X=A[,{2 3}];Y=A[,1];

j=regg(X,Y);print j;

Module Programming (2)

• Create a module for principal componentanalysis in regression (using module definedbefore-nested module)

start rku(cor,p,x,y);n=ncol(cor);call eigen(ac,vc,cor);pac=ac/sum(ac);kpac=pac[1];

do i=2 to n;kpac=kpac||sum(pac[1:i]);end;

if kpac[1]>=p then c=1;else c=0;

do i=2 to n;if kpac[i]>=p thendo;

c=c||1;end;

elsedo;

c=c||0;end;end;

i=1;j=0;k=0;do while(i<=n);

j=j+c[i];if j=1 then k=i;else i=i+1;

end;

acb=ac[1:k];vcb=vc[,1:k];

sku=x*vcb[,1];if k>1 thendo;

do i=1 to (k-1);sku=sku||x*vcb[,i+1];

end;end;

h=regg(sku,y);

return(h);finish;

rho={1 0.9 0.3,0.9 1 0.4,0.3 0.4 1};X={6.1 6.4 4.0,-1.0 -1.0 2.6,2.9 3.0 3.5,-1.1 -1.2 3.4,1.4 1.6 3.8,0.9 1.6 2.2,2.4 2.7 2.5,2.5 3.0 -0.3,4.7 4.3 3.5,4.0 2.4 0.4};y={3,4,2,5,6,1,8,9,3,5};k=rku(rho,0.75,X,y);print k;

Thank you