Linear regression with formulas

Hey, I need to perform a linear regression with the formulas given

x and y with a line above are the average. And this gives the line:

I then need to make a function that takes x and y as arguments and returns the values for the coefficients â and ^b.

Here is my current code:

f = importdata("HadCRUT.4.6.0.0.monthly_ns_avg.txt");
data = f.data(:,1);
dates = f.textdata;
x = datenum(dates, "yyyy/mm");
y = data;

I then know that the function will look like this. After that I dont know how I should proceed, I've tried with a for loop without any success.

function [coeffA,coeffB] = lin_reg(x,y)

end

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Sulaymon Eshkabilov]

Hi,

Here is the solution:

function [a, b] = linear_regression(x,y)
a = sum((x-mean(x)).*(y-mean(y)))./sum((x-mean(x)).^2);
b = mean(y)-a*mean(x);
end

Good luck

[Olaf]

Thanks, do you know how I then can plot y = ax + b inside another plot? Like this:

plox(x,y)
hold on

and then how can I plot the linear regression inside this?

Answer 2

[Sulaymon Eshkabilov]

Hi,

Glad that I was of some help. Pl., click accept of my proposed answer. To plot your lin. reg model, use the following simple code:

x = 0:.1:13;  % just an example
Y_model = a*x+b; plot(x, y, 'bo', x, Y_model, 'r-'), legend('Given Data Set', 'Linear regression fit model')

Good luck