Question

I need this program in MATLAB with different or another code.

INPUT:

x = [0 1 8 12 27];
y = [1 2 3 4 5];


nx = length(x);
ny = length(y);
n = length(x);
if nx ~= ny
display('Error. La cantidad de datos en x no es igual que los datos en y')
end

Sx = sum(x);
Sxx = sum(x.^2);
Sy = sum(y);
Sxy = sum(x.*y);

a1 = (n*Sxy - Sx*Sy)/(n*Sxx-(Sx)^2);
a0 = (Sxx*Sy - Sxy*Sx)/(n*Sxx - (Sx)^2);

m = a1; b = a0;
f = m*x + b;

plot(x,y,'or',x,f,'b')
title('y vs x')
legend('data','regression','Location','SouthOutside')
xlabel('x')
ylabel('y')
display('The values of y in the linear regression is:')
disp(f)

OUTPUT:

The values of y in the linear regression is:
1.6924 1.8286 2.7821 3.3269 5.3701

Answer 1

I have given you two versions of the above code. You can use any one of them.

MATLAB Code

%Data points
x=[0 1 8 12 17];
y=[ 1 2 3 4 5];
%Comparing lengths of x and y
if (length(x)~=length(y))
error('X and Y are of different lengths. Please Check!!!')
else
n=length(x);
end
sx=sum(x);
sx2=sum(x.^2);
sy=sum(y);
sxy=sum(x.*y);
%calculaitng 'm' and 'b'
m=(n*sxy-sx*sy)/(n*sx2-sx^2);
b=(sx2*sy-sxy*sx)/(n*sx2-sx^2);
%y-estimate calculaiton
y_hat=m*x+b;
%Plotting the actual data and estimat
scatter(x,y);
hold on
plot(x,y_hat)
xlabel('x')
ylabel('y')
title('x vs.y')
legend({'Data','Estimate'},'Box','off','Location','northwest')
fprintf('The values of y obtained with Linear Regression is ')
fprintf('%1.4f %1.4f %1.4f %1.4f %1.4f ',y_hat)

Output on the command window

The values of y obtained with Linear Regression is
1.3652 1.5803 3.0860 3.9465 5.0220

MATLAB Code - version 2

The formulas used for 'm' and 'b' are

%Data points
x=[0 1 8 12 17];
y=[ 1 2 3 4 5];
%Comparing lengths of x and y
if (length(x)~=length(y))
error('X and Y are of different lengths. Please Check!!!')
else
n=length(x);
end
mu_x=mean(x);
mu_y=mean(y);
mu_xy=mean(x.*y);
mu_x2=mean(x.^2);
%calculaitng 'm' and 'b'
m=(mu_x*mu_y-mu_xy)/(mu_x^2-mu_x2);
b=mu_y-m*mu_x;
%y-estimate calculaiton
y_hat=m*x+b;
%Plotting the actual data and estimat
scatter(x,y);
hold on
plot(x,y_hat)
xlabel('x')
ylabel('y')
title('x vs.y')
legend({'Data','Estimate'},'Box','off','Location','northwest')
%Displaying the values of estimates on command window
fprintf('The values of y obtained with Linear Regression is ')
fprintf('%1.4f %1.4f %1.4f %1.4f %1.4f ',y_hat)

Output on the command window

The values of y obtained with Linear Regression is
1.3652 1.5803 3.0860 3.9465 5.0220