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10
Multivariate Models
10.1 MULTIPLE LINEAR REGRESSION
We will extend the simple linear regression model to more than one independent variable X. That is,
we now have several (m) independent variables X
i
, inuencing one dependent or response variable Y.
As dened earlier, we develop a linear least squares (LLS) estimator of Y
YbbX bX bX
=+ +++
01122
(10.1)
This is the equation of a plane with intercept b
0
and coefcients b
k
, k = 1, …, m. Note that we now have
m + 1 regression parameters to estimate; these are m coefcients and one intercept. For each observa-
tion i we have a set of data points y
i
, x
ki
, we have the estimated value of Y at t ...