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Linear Regression  part 2 
LINEAR REGRESSION 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 Where COV(X,Y) is the covariance and VAR (X) the variance of X. X is called the dependent variable, and Y the independent. 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. Do you want to know more on the subject? Visit our selection of books 
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