How to summation using for loop with a vector

This is the data used for xi and yi, i have gotten x bar and y bar already, not to sure how to make a for loop for SXY and SXX

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

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

my attempt

SXY = 0;

for [i = 100]

SXY = SXY + (( x(i) - xBar) * ( y(i) - yBar));

end

not sure how to correctly code x(i) and y(i) which should be a new value form the array every time it loops

Answer 1

[Torsten]

rng('default')
n = 100;
x = normrnd(10, 1, 1, n);
y = 1 + 2 .* x + normrnd(0, 1, 1, n);
xbar = mean(x)

xbar = 10.1231

ybar = mean(y)

ybar = 21.1735

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

sxy = 2×2

133.7660 276.2553 276.2553 669.9599

sxy = sxy(2,1)

sxy = 276.2553

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

sxx = 133.7660

Answer 2

[Voss]

"... not to sure how to make a for loop for SXY ..."

The square brackets give you a syntax error:

for [i = 100]

Invalid expression. When calling a function or indexing a variable, use parentheses. Otherwise, check for mismatched delimiters.

Removing them and using the following expression would execute the loop one time, with value i = 100:

for i = 100

To execute the loop 100 times, with values i = 1, i = 2, ..., i = 100, instead, you should do this:

for i = 1:100

Or better:

for i = 1:numel(x)

Once you change the for line, the rest of the code looks like it will work.

However, you don't need to use a for loop to do it. This does the same thing:

SXY = sum(( x - xBar) .* ( y - yBar)) % note: using .* for element-wise multiplication