HP Prime: Best Regression Fit
The program BESTFIT compares a set of regressions to
determine a best fit. This simulates a
feature presented on the Hewlett Packard HP 48S, HP 48G, HP 49G, and HP
50g. BESTFIT compares the correlations
of the following four regression models:
1. Linear: y = a * x + b
2. Logarithmic: y = a * ln x + b
3. Exponential: y = b * a^x
(y = b * e^(ln a * x))
4. Power: y = b * x^a
The output is a two element list: a string of the best fit equation and its
corresponding correlation.
HP Prime Program:
BESTFIT
EXPORT
BESTFIT(L1,L2)
BEGIN
// 2017-11-02 EWS
// Simulate Best Fit
// HP 48GX,49G,50g
// initialize
LOCAL clist,m,c,v,s,n;
clist:={0,0,0,0};
// test
// correlation is linear only
// requires approx()
// linear y=a*x+b
clist[1]:=approx(correlation(L1,L2));
// log y=a*LN(x)+b
c:=approx(correlation(LN(L1),L2));
IF IM(c)==0 THEN
clist[2]:=c;
END;
// exponential y=b*e^(a*x)
c:=approx(correlation(L1,LN(L2)));
IF IM(c)==0 THEN
clist[3]:=c;
END;
// power y=b*a^x
c:=approx(correlation(LN(L1),LN(L2)));
IF IM(c)==0 THEN
clist[4]:=c;
END;
// test
// POS(L0^2,MAX(L0^2))
m:=POS(clist^2,MAX(clist^2));
c:=clist[m];
IF m==1 THEN
v:=linear_regression(L1,L2);
s:=STRING(v[2])+"+"+STRING(v[1])+
"*X";
RETURN {s,c};
END;
IF m==2 THEN
v:=logarithmic_regression(L1,L2);
s:=STRING(v[2])+"+"+STRING(v[1])+
"*LN(X)";
RETURN {s,c};
END;
IF m==3 THEN
v:=exponential_regression(L1,L2);
s:=STRING(v[2])+"*"+STRING(v[1])+
"^X";
RETURN {s,c};
END;
IF m==4 THEN
v:=power_regression(L1,L2);
s:=STRING(v[2])+"*X^"+
STRING(v[1]);
RETURN {v,s};
END;
END;
Examples –
BESTFIT:
Example
1:
|
X
|
y
|
|
1.05
|
10.45
|
|
2.28
|
11.33
|
|
4.20
|
16.38
|
|
6.34
|
28.87
|
Result: {“7.78250037344*1.21713132288^X”, 0.981261724397}
Example 2:
|
X
|
Y
|
|
-10
|
82
|
|
-5
|
41
|
|
5
|
-42
|
|
10
|
-79
|
Result: {“0.5+ -8.1*X”,
-0.999801918343}
Example 3:
|
X
|
Y
|
|
10
|
2.278
|
|
11
|
2.666
|
|
12
|
2.931
|
|
13
|
3.212
|
Result: {“-5.79464870365+3.51429873838*LN(X)”,
0.998295735284}
BESTFIT2: An Extended Version
Version 2 adds the following regressions:
5. Inverse: y = b + a/x
6. Simple
Logistic: y = 1/(b + a*e^(-x))
7. Simple
Quadratic: y = b + a*x^2
8. Square Root: y = √(a*x + b)
HP Prime
Program: BESTFIT2
EXPORT
BESTFIT2(L1,L2)
BEGIN
// 2017-11-02 EWS
// Simulate Best Fit
// HP 48GX,49G,50g
// additional models
// initialize
LOCAL clist,m,c,v,s;
clist:={0,0,0,0,0,0,0,0};
// test
// correlation is linear only
// requires approx()
// linear y=a*x+b
clist[1]:=approx(correlation(L1,L2));
// log y=a*LN(x)+b
c:=approx(correlation(LN(L1),L2));
IF IM(c)==0 THEN
clist[2]:=c;
END;
// exponential y=b*e^(a*x)
c:=approx(correlation(L1,LN(L2)));
IF IM(c)==0 THEN
clist[3]:=c;
END;
// power y=b*a^x
c:=approx(correlation(LN(L1),LN(L2)));
IF IM(c)==0 THEN
clist[4]:=c;
END;
// inverse y=b+a/x
IF POS(L1,0)==0 THEN
clist[5]:=approx(correlation(1/L1,
L2));
END;
// simple logistic
IF POS(L2,0)==0 THEN
clist[6]:=approx(correlation(e^(−L1),
1/L2));
END;
// simple quadratic
clist[7]:=approx(correlation(L1^2,
L2));
// square root
IF ΣLIST(L2≥0)==SIZE(L2) THEN
clist[8]:=approx(correlation(L1,
L2^2));
END;
// test
// POS(L0^2,MAX(L0^2))
m:=POS(clist^2,MAX(clist^2));
c:=clist[m];
IF m==1 THEN
v:=linear_regression(L1,L2);
s:=STRING(v[2])+"+"+STRING(v[1])+
"*X";
END;
IF m==2 THEN
v:=logarithmic_regression(L1,L2);
s:=STRING(v[2])+"+"+STRING(v[1])+
"*LN(X)";
END;
IF m==3 THEN
v:=exponential_regression(L1,L2);
s:=STRING(v[2])+"*"+STRING(v[1])+
"^X";
END;
IF m==4 THEN
v:=power_regression(L1,L2);
s:=STRING(v[2])+"*X^"+
STRING(v[1]);
END;
// inverse
IF m==5 THEN
v:=linear_regression(1/L1,L2);
s:=STRING(v[2])+"+"+STRING(v[1])+
"/X";
END;
// simple logistic
IF m==6 THEN
v:=linear_regression(e^(−L1),
1/L2);
s:="1/("+STRING(v[2])+"+"+
STRING(v[1])+"*e^(−X))";
END;
// simple quadratic
IF m==7 THEN
v:=linear_regression(L1^2,L2);
s:=STRING(v[2])+"+"+STRING(v[1])+
"*X^2";
END;
// square root
IF m==8 THEN
v:=linear_regression(L1,L2^2);
s:="√("+STRING(v[2])+"+"+
STRING(v[1])+"*X)";
END;
RETURN {s,c};
END;
Examples – BESTFIT2:
Example 4:
|
X
|
y
|
|
1.05
|
10.45
|
|
2.28
|
11.33
|
|
4.20
|
16.38
|
|
6.34
|
28.87
|
Result: {“9.0573970192+0.48023219108*X^2”,
0.994491728382}
Example 5:
|
X
|
y
|
|
1
|
8.4853
|
|
2
|
8.9443
|
|
4
|
9.7980
|
|
7
|
10.9546
|
Result: {“√(63.9995089183+8.00048914762*X”, 0.999999999759}
Example 6:
|
X
|
y
|
|
1
|
1
|
|
2
|
-0.5
|
|
3
|
-1
|
|
4
|
-1.25
|
Result: {“-2+3/X”, 1}
Eddie
This blog is property of Edward Shore, 2017
