This preview shows pages 1–3. Sign up to view the full content.
Lecture 13
Lecture component
radj 2
= 1

unexplained variance dfunexplained df
or
radj
2
=
1

=
(

) (  )
=
(

) (  )
i 1n yi yi 2 n p
i 1n yi yi 2 n 1
P is defined as the total number of variables in the regression problem.
ie:
p=m+1
Note that the above formula for
radj 2
is the same as
1
sessy2
where
and
A regression problem has the same number of normal equations to solve as there are
independent variables. (However, some formulations of the normal equations have m + 1
normal equations)
MultiColinearity
is when any 2 or more independent variables are correlated. This
becomes very problematic in multiple regression if the multicolinearity is severe. The
problem occurs in the interpretation of the regression coefficients, standardized or un
standardized.
Let’s take as an example the sale of the house. We have several variables that define
and have influence on
the total price of the house. The price of the house is based on
many different components (like year the home was built, square footage etc., money
spent maintaining the home, etc.) .
Ie:
I once ran a multiple regression equation with selling price of the home as the
dependent variable, with many independent variables. One of the independent variable
was the existence of a garbage disposal (this variable is called a dummy variable, where
the value of 1 indicates the condition exist, and zero indicates that it does not) The
coefficient in front of the dummy variable turned out to be plus $7000. Certainly the
existence of a garbage disposal by itself does not add 7,000 dollars to the value of the
home. It is just an indicator of so much else about the home; the age of the home, the
upkeep of the home, the neighborhood that the home is in, the probability that there are
other conveniences in the home, etc.
The fact that multicolinearity usually exists at some
level means that one should never interpret the regression coefficients in a vacuum. One
has to be extremely careful about their interpretation, especially when high degrees of
multicolinearity exist.
Multiple Regression has no value (no need )if the multicolinearity is nonexistent (no
difficulty separating the influence of one independent variable from the other) meaning
the r
2
between the independent variables is zero, or the correlation matrix of the
independent variables is an identity matrix.
If this is the case then the multiple regression
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document problem could be solved by simply stringing together the simple standardized regression
coefficients from simple linear regression. I
It also has no value if the correlation matrix of the independent variables has nothing but
ones. One could not separate the influence of the socalled independent variables,
because the truth of the matter would be , there is only one independent variable.
Simple Regression
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 08/24/2010 for the course MATH 267 taught by Professor Chandrasekhar during the Summer '10 term at Anna University Chennai  Regional Office, Coimbatore.
 Summer '10
 chandrasekhar
 Statistics, Variance

Click to edit the document details