%nonlinear/multivariable_linea%linear matrix/linear regressi

%nonlinear regresion

clc; clear; close all;

g = @(x) exp(x);
s = @(x) 0.25*exp(x/2);
X = [1, g(2), s(2);
     1, g(3), s(3);
     1, g(5), s(5);
     1, g(10), s(10)];

Y = [2;
     5;
     10;
     17]

 a = ((((X.')*X)^(-1))*(X.'))*Y

 f = @(x) a(1) + a(2)*g(x) + a(3)*s(x);
 x = 0:0.01:10;

 xs = [2,3,5,10];

 figure(1)
    plot(x,f(x)); hold on; grid on;
    plot(xs,Y,'ro'); hold off;


















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%multivariable_linear_regression
clc; clear; close all;

xL=[2 4 6 8 10];
X=[1, 2, 3;
   1, 4, 5;
   1, 5, 7;
   1, 6, 8  ]
Y=[5 ;7; 11; 15]

a = ((((X.')*X)^-1)*(X.'))*Y

k = 1;
f = @(x) a(3)*x + a(2)*x + 1;
x=0:0.01:15;

figure(1)
    plot(x,f(x))

    -1.8 + (-1.4)*4+3*5














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%linear regresion matrix form
clc; clear; close all;

xL=[2 4 6 8 10];
X=[2, 1;
   4, 1;
   6, 1;
   8, 1;
   10, 1]
Y=[5 ;7; 11; 40; 32]

a = ((((X.')*X)^-1)*(X.'))*Y

f = @(x) a(1)*x + a(2)

x = 0:0.1:10;

figure(1)
    plot(x, f(x)); grid on; hold on;
    plot(xL, Y, 'ro'); hold off;
    axis([-1,11,-15,50])








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%liear regression
clc; clear; close all;

x=[2 4 6 8 10];
y=[5 7 11 40 32];
mx=(sum(x))/length(x);
my=(sum(y))/length(y);
for i=1:length(x)
    ap(i)=(x(i)-mx)*(y(i)-my);
    an=sum(ap);
end
for k=1:length(x)
    il(k)=(x(k)-mx)^2;
    ilo=sum(il);
end
a=(an)/(ilo)
b=my-a*mx
wsp=[a,b];
f=a*x+b;
plot(x,y,'ro');
hold on;
plot(x,f,'green'); % rysowanie i kolory
axis([0 20 0 50]);