% Matlab Program to fit straight line/First degree curve (y=ax+b)
clc;
clear;
n=input('\nEnter the value of data entries n= ');
for i=1:1:n
x(i)=input('Enter the values of x= ');
y(i)=input('Enter the values of y= ');
end
sx=0;
sy=0;
sxx=0;
sxy=0;
for i=1:1:n
sx=sx+x(i);
sy=sy+y(i);
sxx=sxx+x(i)*x(i);
sxy=sxy+x(i)*y(i);
end
delta=sxx*n-sx*sx;
delta1=sxy*n-sy*sx;
delta2=sxx*sy-sx*sxy;
a=delta1/delta;
b=delta2/delta;
fprintf('\nThe values of constants a=%f and b=%3f',a,b);
fprintf('\nThe equation of straight line is y=%2.5f x + %2.5f',a,b);
% Plotting best fit curve y=ax+b using points (x, ya) and observed curve using (x, y)
for i=1:1:n
ya(i)=a*x(i)+b; %To find the calculated ya using eq. ya=ax+b as per solution
end
hold on
plot(x,y,'b*-');
plot(x,ya,'r+-');
xlabel('X');
ylabel('Y');
title('Graph of first degree curve using least square criteria');
OUTPUT
Enter the value of data entries n= 7
Enter the values of x= 1
Enter the values of y= 0.5
Enter the values of x= 2
Enter the values of y= 2.5
Enter the values of x= 3
Enter the values of y= 2
Enter the values of x= 4
Enter the values of y= 4
Enter the values of x= 5
Enter the values of y= 3.5
Enter the values of x= 6
Enter the values of y= 6
Enter the values of x= 7
Enter the values of y= 5.5
The values of constants a=0.839286 and b=0.071429
The equation of straight line is y=0.83929 x + 0.07143>>
% Matlab Program to fit second degree curve/parabola/Quadratic Equation (y=ax^2+bx+c)
clc;
clear;
n=input('\nEnter the value no. of data entries n= ');
for i=1:1:n
x(i)=input('Enter the values of x= ');
y(i)=input('Enter the values of y= ');
end
sx=0;
sy=0;
sxx=0;
sxxx=0;
sxxxx=0;
sxy=0;
sxxy=0;
for i=1:1:n
sx=sx+x(i);
sy=sy+y(i);
sxx=sxx+x(i)*x(i);
sxxx=sxxx+x(i)*x(i)*x(i);
sxxxx=sxxxx+x(i)*x(i)*x(i)*x(i);
sxy=sxy+x(i)*y(i);
sxxy=sxxy+x(i)*x(i)*y(i);
end
delta=sxxxx*(sxx*n-sx*sx)-sxxx*(sxxx*n-sxx*sx)+sxx*(sxxx*sx-sxx*sxx);
delta1=sxxy*(sxx*n-sx*sx)-sxxx*(sxy*n-sy*sx)+sxx*(sxy*sx-sy*sxx);
delta2=sxxxx*(sxy*n-sy*sx)-sxxy*(sxxx*n-sxx*sx)+sxx*(sxxx*sy-sxx*sxy);
delta3=sxxxx*(sxx*sy-sx*sxy)-sxxx*(sxxx*sy-sxx*sxy)+sxxy*(sxxx*sx-sxx*sxx);
a=delta1/delta;
b=delta2/delta;
c=delta3/delta;
fprintf('\nThe values of constants a=%f ,b=%f and c=%f',a,b,c);
fprintf('\nThe equation of second degree curve is y=%2.3f x^2 + %2.3f x +
%2.3f',a,b,c);
% Plotting best fit curve y=ax^2+bx+c using points (x,ya)& observed curve using (x, y)
for i=1:1:n
ya(i)=a*x(i)*x(i)+b*x(i)+c; %To find the calculated ya using equation
ya=ax^2+bx+c
end
hold on
plot(x,y,'b*-');
plot(x,ya,'r+-');
xlabel('X');
ylabel('Y');
title('Graph of second degree curve using least square criteria');
OUTPUT
Enter the value no. of data entries n= 7
Enter the values of x= -3
Enter the values of y= 12
Enter the values of x= -2
Enter the values of y= 4
Enter the values of x= -1
Enter the values of y= 1
Enter the values of x= 0
Enter the values of y= 2
Enter the values of x= 1
Enter the values of y= 7
Enter the values of x= 2
Enter the values of y= 15
Enter the values of x= 3
Enter the values of y= 30
The values of constants a=2.119048 ,b=2.928571 and c=1.666667
The equation of second degree curve is y=2.119 x^2 + 2.929 x + 1.667>>
% Matlab Program to fit an exponential curve a*e^bx
clc;
n=input('\nEnter the value no. of data entries n= ');
for i=1:1:n
x(i)=input('Enter the values of x= ');
y(i)=input('Enter the values of y= ');
Y(i)=log(y(i));
X(i)=x(i);
end
sx=0;
sy=0;
sxx=0;
sxy=0;
for i=1:1:n
sx=sx+X(i);
sy=sy+Y(i);
sxx=sxx+X(i)*X(i);
sxy=sxy+X(i)*Y(i);
end
delta=sxx*n-sx*sx;
delta1=sxy*n-sy*sx;
delta2=sxx*sy-sx*sxy;
a1=delta1/delta;
b1=delta2/delta;
a=exp(b1);
b=a1;
fprintf('\n The values of constants a1=%f and b1=%f',a1,b1);
fprintf('\n The values of constants a=%f and b=%f',a,b);
fprintf('\n The equation of exponential curve is y=%2.4fe^%2.4fx',a,b);
% Plotting best fit curve y=ae^bx using points (x, ya) and observed curve using (x, y)
for i=1:1:n
ya(i)=a*exp(b*x(i)); %To find the calculated ya using equation ya=aebx
end
hold on
plot(x,y,'b*-')
plot(x,ya,'r*--')
xlabel('X');
ylabel('Y');
title('Graph of exponential curve using least square criteria');
OUTPUT
Enter the value no. of data entries n= 4
Enter the values of x= 0.1
Enter the values of y= 1.832
Enter the values of x= 0.2
Enter the values of y= 2.238
Enter the values of x= 0.3
Enter the values of y= 2.733
Enter the values of x= 0.4
Enter the values of y= 3.338
The values of constants a1=1.999708 and b1=0.405514
The values of constants a=1.500073 and b=1.999708
The equation of exponential curve is y=1.5001e^1.9997x>>
% Matlab Program to fit power equation ax^b
clc;
n=input('\nEnter the value no. of data entries n= ');
for i=1:1:n
x(i)=input('Enter the values of x= ');
y(i)=input('Enter the values of y= ');
X(i)=log10(x(i));
Y(i)=log10(y(i));
end
sx=0;
sy=0;
sxx=0;
sxy=0;
for i=1:1:n
sx=sx+X(i);
sy=sy+Y(i);
sxx=sxx+X(i)*X(i);
sxy=sxy+X(i)*Y(i);
end
delta=sxx*n-sx*sx;
delta1=sxy*n-sy*sx;
delta2=sxx*sy-sx*sxy;
a1=delta1/delta;
b1=delta2/delta;
a=10^b1;
b=a1;
fprintf('\nThe values of constants a1=%f and b1=%f',a1,b1);
fprintf('\nThe values of constants a=%f and b=%f',a,b);
fprintf('\nThe power equation is y=%2.4f x^ %2.4f',a,b);
% Plotting best fit curve y=ax^b using points (x, ya) and observed curve using (x, y)
for i=1:1:n
ya(i)=a*power(x(i),b); %To find the calculated ya using equation ya= ax^b
end
hold on
plot(x,y,'b*-')
plot(x,ya,'r*--')
xlabel('X');
ylabel('Y');
title('Graph of power function y=ax^b curve using least square criteria');
OUTPUT
Enter the value no. of data entries n= 5
Enter the values of x= 1
Enter the values of y= 0.5
Enter the values of x= 2
Enter the values of y= 2
Enter the values of x= 3
Enter the values of y= 4.5
Enter the values of x= 4
Enter the values of y= 8
Enter the values of x= 5
Enter the values of y= 12.5
The values of constants a1=2.000000 and b1=-0.301030
The values of constants a=0.500000 and b=2.000000
The power equation is y=0.5000 x^ 2.0000>>
% Matlab Program to fit power equation ab^x
clc;
n=input('\nEnter the value no of data entries,n= ');
for i=1:1:n
x(i)=input('Enter the values of x= ');
y(i)=input('Enter the values of y= ');
Y(i)=log10(y(i));
X(i)=x(i);
end
sx=0;
sy=0;
sxx=0;
sxy=0;
for i=1:1:n
sx=sx+X(i);
sy=sy+Y(i);
sxx=sxx+X(i)*X(i);
sxy=sxy+X(i)*Y(i);
end
delta=sxx*n-sx*sx;
delta1=sxy*n-sy*sx;
delta2=sxx*sy-sx*sxy;
a1=delta1/delta;
b1=delta2/delta;
a=10^a1;
b=10^b1;
fprintf('\nThe values of constants a1=%f and b1=%f',a1,b1);
fprintf('\nThe values of constants a=%f and b=%f',a,b);
fprintf('\nThe power equation is y=%2.4f * %2.4f ^x',a,b);
% Plotting best fit curve y=ab^x using points (x, ya) and observed curve using (x, y)
for i=1:1:n
ya(i)=a*power(b,x(i)); %To find the calculated ya using equation ya=ab^x
end
hold on
plot(x,y,'b*-')
plot(x,ya,'r*--')
xlabel('X');
ylabel('Y');
title('Graph of power function y=ab^x curve using least square criteria');
OUTPUT
Enter the value no of data entries,n= 4
Enter the values of x= 1
Enter the values of y= 4
Enter the values of x= 2
Enter the values of y= 11
Enter the values of x= 3
Enter the values of y= 35
Enter the values of x= 4
Enter the values of y= 100
The values of constants a1=0.469650 and b1=0.122756
The values of constants a=2.948829 and b=1.326650
The power equation is y=2.9488 * 1.3266 ^x>>
