Estimate for Residual variance function calculation

Hi, need some help on how to code residual varience, i have the formula and have attached code that i have so far, note slope = B1, intercept = B0

%data

x = normrnd(10, 1, 1, 100);

y = 1 + 2 .* x + normrnd(0, 1, 1, 100);

n = 100;

xBar = mean(x);

yBar = mean(y);

%slope

sxy = cov(x,y) * (n-1);

sxy = sxy(2,1);

sxx = var(x) * (n-1);

slope = sxy/sxx;

%intercept

intercept = yBar - (slope * xBar);

%residual varience

frontThing = 1/n-2;

Answer 1

[Torsten]

x = normrnd(10, 1, 1, 100);
y = 1 + 2 .* x + normrnd(0, 1, 1, 100);
n = 100;
xBar = mean(x);
yBar = mean(y);
%slope
sxy = cov(x,y) * (n-1);
sxy = sxy(2,1);
sxx = var(x) * (n-1);
slope = sxy/sxx;
%intercept
intercept = yBar - (slope * xBar); 
%residual variance
yhat = intercept + slope*x;
residual_variance = (n-1)/(n-2)*var((y-yhat).^2)

residual_variance = 1.5632

[Abolfazl Chaman Motlagh]

the var get the variance of vector itself. by the difinition of formula you should take sum over it !!

which is not the formula is.

i think the correct one is :

residual_variance = (1/(n-2))*sum((y-yhat).^2)

ans if you want to have , you should take sqrt from above value.

residual_variance = sqrt((1/(n-2))*sum((y-yhat).^2))

[Torsten]

You are right - should be

rng('default')
x = normrnd(10, 1, 1, 100);
y = 1 + 2 .* x + normrnd(0, 1, 1, 100);
n = 100;
xBar = mean(x);
yBar = mean(y);
%slope
sxy = cov(x,y) * (n-1);
sxy = sxy(2,1);
sxx = var(x) * (n-1);
slope = sxy/sxx;
%intercept
intercept = yBar - (slope * xBar); 
%residual variance
yhat = intercept + slope*x;
residual_variance = 1/(n-2)*(y-yhat)*(y-yhat).'

residual_variance = 1.0146