Question

Explanation and complete code gets thumbs up. For this Matlab problem. For this problem, use Matlab to plot the data and the best fit. Show the written solutions and the Matlab graphs.

Problem Use least squares regression to fit a straight line to r 0246911 121517 19 y567698710 12 12 Along with the slope and intercept, compute the correlation coefficient. Plot the data and the regression line. Then repeat the problem, but regress x versus y - that is, switch the variables.

Answer 1

Executable code:

clc;
clear all;
close all;
x=[0 2 4 6 9 11 12 15 17 19]
y=[5 6 7 6 9 8 7 10 12 12]
a=sum((x-mean(x)).*(y-mean(y)));
b=sum((x-mean(x)).^2);
slope=a/b
intercept=mean(y)-slope*mean(x)
p=[slope intercept];
Y_estimated=polyval(p,y);
n=numel(y);
Std_Error_Estimate=sqrt((sum(y-Y_estimated).^2)/n)
correlation_coefficient=(n*sum(x.*y)-(sum(x)*sum(y)))/((sqrt(n*sum(x.^2)-(sum(x))^2))*sqrt((n*sum(y.^2)-(sum(y))^2)))
plot(x,Y_estimated,'m')
hold on
plot(x,y,'b*')
legend('regression line','data')

Output:

12 r 11F 10 8 10 15 20