its a good ppt for study

1. TOPIC
MULTIPLE REGRESSION
ANALYSIS
Swami Vivekananda Institute of Modern Science
Presented to: Dr. Meghdoot Ghosh
Presented by: Arnab Naskar
Roll no: 26405020106
Registration No: 202642005010005
Department: BBA
Semester: 5th SEM

2. Multiple regression is a statistical technique
that can be used to analyze the relationship
between a single dependent variable and
several independent variables.
DEFINATION

3. One dependent variable (criterion)
Two or more independent variables
(predictor variables).
Sample size: >= 50 (at least 10 times
as many cases as independent
variables)
DESIGN REQUIREMENTS

4.  Independence: the scores of any particular subject are
independent of the scores of all other subjects
 Normality: in the population, the scores on the dependent
variable are normally distributed for each of the possible
combinations of the level of the X variables; each of the
variables is normally distributed
 Homoscedasticity: in the population, the variances of the
dependent variable for each of the possible combinations
of the levels of the X variables are equal.
 Linearity: In the population, the relation between the
dependent variable and the independent variable is linear
when all the other independent variables are held
constant.
ASSUMPTIONS

5.  One dependent variable Y
predicted from one
independent variable X
 One regression coefficient
 r2: proportion of variation
in dependent variable Y
predictable from X
 One dependent variable Y
predicted from a set of
independent variables (X1,
X2 ….Xk)
 One regression coefficient
for each independent
variable
 R2: proportion of variation
in dependent variable Y
predictable by set of
independent variables
(X’s)
SIMPLE VS. MULTIPLE
REGRESSION

6. PROPORTION OF PREDICTABLE
AND UNPREDICTABLE VARIATION
X1
Y
(1-R2) = Unpredictable
(unexplained) variation
in Y
X2
Where:
Y= AA
X1 = ASC
X2 =GSC
R2 = Predictable
(explained)
variation in Y

7.  Testing R2
Test R2 through an F test
Test of competing models (difference between
R2) through an F test of difference of R2s
 Testing b
Test of each partial regression coefficient (b) by
t-tests
Comparison of partial regression coefficients
with each other - t-test of difference between
standardized partial regression coefficients ()
VARIOUS SIGNIFICANCE
TESTS

8. THANK YOU