If we look at the errors, we see that they are dependent on the value of x! Naturally (b/c of mean=x[i]).

What I

*should*have done is something like this:

Nevertheless, I hope the essential points are clear:

**• covariance is related to variance: cov(x,x) = var(x)**

• correlation is the covariance of z-scores

• the slope of the regression line is: cov(x,y) / var(x)

• the regression line goes through x, y

• r ≈ cov(x,y) / sqrt(var(x)*var(y))

• the call to plot the line is abline(lm(y~x))

• correlation is the covariance of z-scores

• the slope of the regression line is: cov(x,y) / var(x)

• the regression line goes through x, y

• r ≈ cov(x,y) / sqrt(var(x)*var(y))

• the call to plot the line is abline(lm(y~x))

The proportionality for r is b/c we are not matching R's output for this. I think it is because we are missing a correction factor of n-1/n. I will have to look into that when I get back to my library at home.

With the change, we do a little better on guessing the slope:

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