Statistics 231B SAS Practice Lab #2
Spring 2006
This lab is designed to give the students practice in fitting multiple linear regression
model and testing regression relation, obtaining scatter plot matrix, correlation matrix and
box plot for diagnostic purpose, calculate the coefficient of multiple determination R2 and
coefficient of simple determination.
Example: In a small-scale experimental study of the relation between degree of
brand liking (Y) and moisture content (X1) and sweetness (X2) of the product, the
data were obtained from the experiment based on a completely randomized
design, see CH06PR05.txt.
To study this relationship, we can first set up
A Multiple Regression Model: First Order Model with Two Predictor Variables
Y X X
i i i i
0 1 1 2 2
with Response function as
22110
XXYE
Meaning of Regression Coefficients
tscoefficien regression partial called are ,
21
In this example, when X1 changes, the change in Y is the same no matter what level X2
is held at, and vice versa. Such a model is called an additive effects model and the
predictors do not interact in the effects on Y.
Is it reasonable to assume this first order regression model? We can use
Scatter Plot Matrix and the Correlation Matrix to get some feeling about the nature and
strength of the bivariate relationship between each of the predictor variables and the
response variable and in identifying gaps in the data points as well as outlying data
points. A correlation matrix contains the coefficient of simple correlation between Y and
each of the predictor variables, as well as all of the coefficients of simple correlation
among the predictor variables. It is a complement to the scatter plot matrix.
(1) Obtain the scatter plot matrix and the correlation matrix.
SAS CODE:
constant held isX and 1X when }Y{E
constant held is X and 1X when }Y{E
mode of rangein 0X,0X ifonly
YE responsemean intercept, theis
122
211
21
0
