Correlation coefficient(r) and the residual(e)

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.

 

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