Polynomial regression: Difference between revisions

=={{header|AWK}}==

{{trans|Lua}}

<lang AWK>

BEGIN{

i = 0;

xa[i] = 0; i++;

xa[i] = 1; i++;

xa[i] = 2; i++;

xa[i] = 3; i++;

xa[i] = 4; i++;

xa[i] = 5; i++;

xa[i] = 6; i++;

xa[i] = 7; i++;

xa[i] = 8; i++;

xa[i] = 9; i++;

xa[i] = 10; i++;

i = 0;

ya[i] = 1; i++;

ya[i] = 6; i++;

ya[i] = 17; i++;

ya[i] = 34; i++;

ya[i] = 57; i++;

ya[i] = 86; i++;

ya[i] =121; i++;

ya[i] =162; i++;

ya[i] =209; i++;

ya[i] =262; i++;

ya[i] =321; i++;

exit;

}

{

# (nothing to do)

}

END{

a = 0; b = 0; c = 0; # globals - will change by regression()

regression(xa,ya);

printf("y = %6.2f x^2 + %6.2f x + %6.2f\n",c,b,a);

printf("%-13s %-8s\n","Input","Approximation");

printf("%-6s %-6s %-8s\n","x","y","y^")

for (i=0;i<length(xa);i++) {

printf("%6.1f %6.1f %8.3f\n",xa[i],ya[i],eval(a,b,c,xa[i]));

}

}

function eval(a,b,c,x) {

return a+b*x+c*x*x;

}

# locals

function regression(x,y, n,xm,ym,x2m,x3m,x4m,xym,x2ym,sxx,sxy,sxx2,sx2x2,sx2y) {

n = 0

xm = 0.0;

ym = 0.0;

x2m = 0.0;

x3m = 0.0;

x4m = 0.0;

xym = 0.0;

x2ym = 0.0;

for (i in x) {

xm += x[i];

ym += y[i];

x2m += x[i] * x[i];

x3m += x[i] * x[i] * x[i];

x4m += x[i] * x[i] * x[i] * x[i];

xym += x[i] * y[i];

x2ym += x[i] * x[i] * y[i];

n++;

}

xm = xm / n;

ym = ym / n;

x2m = x2m / n;

x3m = x3m / n;

x4m = x4m / n;

xym = xym / n;

x2ym = x2ym / n;

sxx = x2m - xm * xm;

sxy = xym - xm * ym;

sxx2 = x3m - xm * x2m;

sx2x2 = x4m - x2m * x2m;

sx2y = x2ym - x2m * ym;

b = (sxy * sx2x2 - sx2y * sxx2) / (sxx * sx2x2 - sxx2 * sxx2);

c = (sx2y * sxx - sxy * sxx2) / (sxx * sx2x2 - sxx2 * sxx2);

a = ym - b * xm - c * x2m;

}

</lang>

{{out}}

<pre>

y = 3.00 x^2 + 2.00 x + 1.00

Input Approximation

x y y^

0.0 1.0 1.000

1.0 6.0 6.000

2.0 17.0 17.000

3.0 34.0 34.000

4.0 57.0 57.000

5.0 86.0 86.000

6.0 121.0 121.000

7.0 162.0 162.000

8.0 209.0 209.000

9.0 262.0 262.000

10.0 321.0 321.000

</pre>