Is the regression line good? We need to check the mean and std of x and the mean and std y.
r = ((1/n)(∑xi-x¯)/sx) (∑yi -ȳ)/sy = ((1/n)(∑xi-x¯)/sqrt(xi-x¯/n))(∑yi -ȳ)/sqrt(∑yi -ȳ/n)
r= (1/n-1) ∑Zscore(xi)Zscore(yi)
[-1,1] is the range/interval of the residual/correlation coefficient when r=-1 or r=1 represent that each point will lie exactly on the regression line.
If the residual(r) is above +0 than the slope is positive if it it above +0.5 it is also a strong correlation, opposite is true for -0 and -0.5.
Residual = Actual – Predicted.
The regression line minimize the residuals to a sum total of (∑e)= 0 because all the negative residuals and positive cancel each other. It also makes the residual mean(ē) equal to 0.
