## Multiple Regression

## Forrest Young's Notes

## Copyright © 1997-9 by Forrest W. Young.

## Linear Combinations: Example

Much of multivariate analysis is concerned with linear combinations of variables. Consider the following three observations on two variables:

X1X2obs12 4 obs25 2 obs31 2 We can create a new variable Y that is a linear combination of the two X's by multiplying each of the original variables by a constant and adding the products.

Let's say we arbitrarily select mutiplicands of 3 and 2. Then we have: Y = 3(X

1) + 2(X2)And we have

Y = [14 19 7]

Here is a schematic of the geometry of the linear combination above. Notice that the result of the linear combination Y, is shown, both in the schematic and in the table below it. ## Geometry of Linear Combinations

X1X2Y obs12 4 14 obs25 2 19 obs31 2 7