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Linear Regression - part 2
As we have seen in the previous page, the above graph illustrate the equation:
X = a + b Y
What we are missing in this equation is the distance between the observations (blue points) and the line. This distance is called 'regression residuals'.
The statistical equation is:
X = a + b Y + u
Where u is the regression residual.
a and b are determined such that the sum of the squared distances of all the data points from the line (u) is the lowest possible.
We can demonstrate that:
b = COV(X,Y) / VAR X
a = X - b Y
With a bit of imagination, we can extend the formula to several independent variables. The formula therefore is:
X = a + b Y + c Z + d W + ... + u
ATTENTION : the above formula are applicable only if u follows certain rules we will explain in the next section.
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