This presentation discusses the application of logistic model in sports research. One can understand the model and the procedure involved in developing it if the assumptions for this analysis is satisfied.

1. Presentation on Chapter 11
Presented by
Dr.J.P.Verma
MSc (Statistics), PhD, MA(Psychology), Masters(Computer Application)
Professor(Statistics)
Lakshmibai National Institute of Physical Education, Gwalior, India
(Deemed University)
Email: vermajprakash@gmail.com

2. Logistic Regression
What it is?
A statistical technique of predicting group membership of a dichotomous
dependent variable on the basis of independent variables.
2

3. What it Does?
It develops a predictive model when the dependent variable is
dichotomous and independent variables are categorical
Logistic Regression
3

4. Assumptions about Variables
Dependent Variable Dichotomous (1,0)
1 : Happening of event like success of penalty stroke, winning
in match, passing minimum muscular fitness test
0: Non happening of event
Independent Variable Nominal variable
Can be ratio, interval, or mix of metric or non-metric
4

5. 5
This Presentation is based on
Chapter 11 of the book
Sports Research with Analytical
Solution Using SPSS
Published by Wiley, USA
Complete Presentation can be accessed on
Companion Website
of the Book
Request an Evaluation Copy For feedback write to vermajprakash@gmail.com

6. What we do in Logistic Regression?
We develop a model for
predicting
Probability, p
(dependent variable takes
value 1 rather than 0)
on the
basis of
Independent
variables
6

7. Predicting probability p
nn22110 xb.........xbxbbp 
Can p be the linear function of
independent variables ?
Due to large number of IVs the p may
exceed 1 which is not permissible.
What to do ?
No
7

8. Predicting the probability p in Logistic Regression?
Instead of p
Log(Odds) is predicted
On the basis of IVs
zxbb
pˆ1
pˆ
log 110 






Log(Odds) or Logit
Probability, p is predicted by knowing Log(Odds)
8

9. Predicting p with Log(Odds)
zxbb
pˆ1
pˆ
log 110 






zxbb
ee
pˆ1
pˆ 10



z
z
xbb
xbb
e1
e
e1
e
pˆ
10
10



 

By knowing z the probability can be estimatedpˆ
9

10. Advantage of using Log(Odds) function
z
z
xbb
xbb
e1
e
e1
e
pˆ
10
10



 

)z(fpˆ  3322110 xbxbxbbz 
- 0
1
0.5
 + 
z
p
Whatever may be the value of Z, the p will vary between 0 and 1 10

11. Regression analysis Vs Logistic regression
Simple Regression
xbby 10 
For each unit increase in x, the y
increases by b1 units
Example: y= 2+3x
x y
1 5
2 8
3 11
4 14
Logistic Regression
xbb
pˆ1
pˆ
log)Odds(Log 10 







For each unit increase in x, the
Log(Odds) increases by ‘b’ units.
Or
pˆ1
pˆ
Odds


increases by
Exp(b1)
11

12. Application in Sports Research
 Predicting penalty kick success in hockey on the basis of IVs such as
speed of the hit, player’s height, accuracy, arm strength and eye hand
coordination etc.
 Predicting winning in football match on the basis of IVs like number of
passes, number of turnovers, penalty yardage, fouls committed etc.,
 Finding likelihood of a particular horse finishing first in a specific race.
12

13. Assumptions
1. Dependent variable is binary in nature.
2. Independent variables can be categorical, numerical or mix of it.
3. Logit transformation of the dependent variable has a linear
relationship with the independent variables.
4. At least 10 sample per independent variable required.
13

14. Steps in Logistic Regression
1. Code dependent variable
1 : occurrence of an event
0 : otherwise
2. Define Code for categorical IVs
Code may be 0,1,2 or any sequence
Highest code for reference category
14

15. Steps in Logistic Regression
3. Use SPSS to generate the following output
a. Coding of dependent and independent variables
b. Omnibus Tests of Model Coefficients
c. Model Summary
d. Hosmer and Lemeshow Test
e. Classification Tablea
f. Variables in the equation
g. Variables not in the equation
15

16. Steps in Logistic Regression
4. Develop logistic regression equation
using regression coefficient of the variables
selected in the model for predicting log(odds)
5. Report the findings using Exp(B)
16

17. Logistic Regression with SPSS
Objective: Predicting success in basketball match
____________________________________________
Match Result Number of Offensive Free throws Blocks
Pass rebound throws
1 1 0 1 1 1
2 0 1 0 0 0
3 1 0 1 1 0
4 1 1 0 0 1
5 0 1 1 1 0
6 0 0 0 0 1
7 1 1 0 1 0
8 0 0 1 0 1
9 1 1 0 1 1
10 0 1 1 0 0
11 1 0 0 1 0
12 0 1 0 0 1
13 1 1 1 1 0
14 0 0 0 0 1
15 1 1 1 1 0
16 0 0 0 1 1
17 0 1 1 0 0
18 1 0 0 1 1
19 0 1 1 0 0
20 1 0 0 1 0
21 0 1 1 0 1
22 1 0 0 1 1
__________________________________________________________________
Dependent Variable
Independent Variable
Result in Basketball Match:
1: Win
0:Loose
No. of pass : 1 = lower 0 = higher
Offensive rebound : 1 = lower 0 = higher
Free throws : 1 = lower 0 = higher
Blocks : 1 = lower 0 = higher
 Team having average number of pass less than the opponent is coded as 1 and the other as 0.
 Similar coding for other variables
- An Illustration
17

18. Step 1: Defining Variables
3
Define long name of the
variables in this column
Click on
Variable View
1
Define short
name of the
variables in this
column
2
6 Define type of variable
in this column
Define code in the window by clicking
on this cell and then click on Add and
OK in the window
1: Loss
2: Win
4
Define code
for other
variables as
well
5
Logistic Regression with SPSS
18

19. 19
To buy the book
Sports Research With Analytical
Solutions Using SPSS
and all associated presentations click Here
Complete presentation is available on
companion website of the book
For feedback write to vermajprakash@gmail.comRequest an Evaluation Copy