Your Financial Tutorial

Financial Statistics: Linear Regression - part 2
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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.