Multiple Regression

BUSINESS STATISTICS Multiple Regression



9 Multiple Regression
• Using Statistics
• The k-Variable Multiple Regression Model
• The F Test of a Multiple Regression Model
• How Good is the Regression
• Tests of the Significance of Individual
Regression Parameters



ssoc. Prof. Ho Thanh Phong 9-1 School of Business – International University

,BUSINESS STATISTICS Multiple Regression


9-1 Using Statistics

y Lines y Planes
B

B
A



Slope: 1 C
A
x1
Intercept: 0

x2
x
Any two points (A and B), or Any three points (A, B, and C), or an
an intercept and slope (0 and intercept and coefficients of x1 and x2
1), define a line on a two- (0 , 1, and 2), define a plane in a
dimensional surface. three-dimensional surface.


ssoc. Prof. Ho Thanh Phong 9-2 School of Business – International University

, BUSINESS STATISTICS Multiple Regression

9-2 The k-Variable Multiple Regression
Model
The population regression model of a
x2
dependent variable, Y, on a set of k y
independent variables, X1, X2,. . . , Xk is 2
given by:
Y= 0 + 1X1 + 2X2 + . . . + kXk +
1
where 0 is the Y-intercept of the 0
regression surface and each i , i = 1,2,...,k
is the slope of the regression surface - x1
sometimes called the response surface - y   0   1 x1   2 x 2  
with respect to Xi.
Model assumptions:
1. ~N(0,2), independent of other errors.
2. The variables Xi are uncorrelated with the error term.

ssoc. Prof. Ho Thanh Phong 9-3 School of Business – International University