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Logistic Regression An Application in Sports
Presentation on Chapter 11
Presented by
Dr.J.P.VermaMSc (Statistics), PhD, MA(Psychology), Masters(Computer Application)
Professor(Statistics)Lakshmibai National Institute of Physical Education,
Gwalior, India(Deemed University)
Email: [email protected]
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Logistic Regression
What it is?
A statistical technique of predicting group membership of a dichotomous dependent variable on the basis of independent variables.
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What it Does?
It develops a predictive model when the dependent variable is dichotomous and independent variables are categorical
Logistic Regression
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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
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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 [email protected]
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What we do in Logistic Regression?
We develop a model
forpredicting
Probability, p (dependent variable takes value 1 rather than 0)
on the basis of
Independent variables
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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
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Predicting the probability p in Logistic Regression?
Instead of p
Log(Odds) is predicted
On the basis of IVs
zxbbp̂1
p̂log 110
Log(Odds) or Logit
Probability, p is predicted by knowing Log(Odds)
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Predicting p with Log(Odds)
zxbbp̂1
p̂log 110
zxbb eep̂1
p̂10
z
z
xbb
xbb
e1e
e1ep̂
10
10
By knowing z the probability can be estimatedp̂
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Advantage of using Log(Odds) function
z
z
xbb
xbb
e1e
e1ep̂
10
10
)z(fp̂ 3322110 xbxbxbbz
- 0
1
0.5
+ z
p
Whatever may be the value of Z, the p will vary between 0 and 1
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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 y1 52 83 114 14
Logistic Regression
xbbp̂1
p̂log)Odds(Log 10
For each unit increase in x, the Log(Odds) increases by ‘b’ units. Or
p̂1p̂Odds
increases by Exp(b1)
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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.
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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.
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Steps in Logistic Regression
1. Code dependent variable1 : occurrence of an event 0 : otherwise
2. Define Code for categorical IVsCode may be 0,1,2 or any sequenceHighest code for reference category
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Steps in Logistic Regression
3. Use SPSS to generate the following output
a. Coding of dependent and independent variablesb. Omnibus Tests of Model Coefficientsc. Model Summaryd. Hosmer and Lemeshow Teste. Classification Tablea
f. Variables in the equationg. Variables not in the equation
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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)
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Logistic Regression with SPSSObjective: Predicting success in basketball match____________________________________________Match Result Number of Offensive Free throws Blocks
Pass rebound throws
1 1 0 1 1 12 0 1 0 0 03 1 0 1 1 04 1 1 0 0 15 0 1 1 1 06 0 0 0 0 17 1 1 0 1 08 0 0 1 0 19 1 1 0 1 110 0 1 1 0 011 1 0 0 1 012 0 1 0 0 113 1 1 1 1 014 0 0 0 0 115 1 1 1 1 016 0 0 0 1 117 0 1 1 0 018 1 0 0 1 119 0 1 1 0 020 1 0 0 1 021 0 1 1 0 122 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 = higherFree 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
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Step 1: Defining Variables
3Define long name of the variables in this column
Click on Variable View
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Define short name of the variables in this column
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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 window1: Loss2: Win
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Define code for other variables as well
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Logistic Regression with SPSS
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