HP Prime and TI-84 Plus CE: Cosine Regression

HP Prime and TI-84 Plus CE:  Cosine Regression

Introduction

The program COSREG attempts to fit data to the curve:

Y = A*cos(C*(X-D)) +B

The user will provide the x-data, y-data, and the period of the data.  Radians mode will be used. 

HP Prime Program: COSREG

Arguments  x list, y list, estimated period

EXPORT COSREG(L1,L2,P)

BEGIN

// EWS 2017-07-25

// x list, y list, period

// Estimated Cosine Regression

// Y = A*COS(C(X-D))+B

// Radians mode

HAngle:=0;

LOCAL C:=2*π/P;

LOCAL I:=POS(L2,MAX(L2));

LOCAL D:=L1(I);

LOCAL S:=SIZE(L1);

LOCAL L0:=MAKELIST(1,X,1,S);

L1:=COS(C*L1-D);

LOCAL M1,M2,M3;

M1:=list2mat(CONCAT(L0,L1),S);

M1:=TRN(M1);

M2:=list2mat(L2,S);

M2:=TRN(M2);

M3:=CAS.LSQ(M1,M2);

LOCAL A:=M3[2,1];

LOCAL B:=M3[1,1];

RETURN {"A*COS(C(X-D))+B",

A,C,D,B};

END;

TI-84 Plus CE Program:  COSREG

"EWS 2017-07-26"

Disp "COSINE FIT"

Disp "A*cos(C*(X-D))+B"

Radian

Input "X: ",L1

Input "Y: ",L2

Input "PERIOD: ",C

2π/C→C

0→K

Repeat L2(K)=max(L2)

K+1→K

End

L1(K)→D

cos(C*L1-D)→L1

LinReg(a+bx) L1,L2

Disp "{A,C,D,B}"

Pause {a,C,D,b}

Disp "r=",r

The coefficients are returned in a list.

Cosine Regression: Y = A * COS(C*(X – D)) + B

Example 1

X = {0, π/4, π/2, 3π/4 ,1}

Y = {5, 2, -1, 2, 5}

Period:  π

Results:

A = 3

C = 2

D = 0

B = 2

(TI-84 Plus CE:  r = 1)

(Y = 2 COS(2X) + 3 – exact match)

Example 2

X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

Y = {2.5, 4.2, 6.8, 4.4, 2.24, 4.35, 7, 4.41, 2.6, 4.2, 6.76, 4.48}

Period = 4

Results:

A = 4.495

C = 1.570796327

D = 7
B = -1.37970927

(TI-84 Plus CE:  r = -0.6213278417)

(An OK… fit)

Eddie

This blog is property of Edward Shore, 2017