Logistic regression can be used to model categorical outcomes, such as whether a patient will live or die after being admitted to the hospital. It involves calculating the odds ratio of an event occurring compared to it not occurring, and taking the log of the odds ratio. This allows the relationship between independent variables and a binary dependent variable to be modeled.

2. Will a patient live or die after being admitted to a
hospital?
I don’t Know
But this is an issue which will help me to understand
Logistic regression as it is the way that can be used to model
categorical outcomes such as this.

4. Logistic Regression Regression
Independent
Variable
Dependent
Variable
Example
Quantitative,
Qualitative
Qualitative
Quantitative,
Qualitative
Quantitative
Result (Pass, Fail) is
the function of time
given to study
Marks obtained is
the function of time
given to study

5. Binomial Distribution
Data Qualitative Data with two categories
Number of
Trials
Fixed or known
Relation
betweenTrials
Independent
Probability Constant Probability of Success & Failure

6. Marks
Study
Hours
Passing
Marks
Study
Hours
Result
Pass
Fail
Logistic RegressionRegression

7. What is Logistic Regression?

8. Probability Odd Ratio
Let there be 7 chances of success and 3 chances of failure
out of total 10 chances
Chances of event / Chances
of not Event
Chances of event / Total
Chances
.01
.1
.5
.6
.9
.99
1:99
1:9
1:1
3:2
9:1
99:1
Change the Given
Probabilities into Odd ratio

9. Probability Odd Ratio
Log Odd Ratio
Logit Ratio
Formula
Values
.01
.1
.5
.6
.9
.99
1:99
1:9
1:1
3:2
9:1
99:1
-4.59
-2.20
0
.41
2.20
4.59

12. Logistic RegressionTheory

13. Different Methods to Express Logistic Regression
Odd Ratio
Form
Logit form
Conditional
Probability
form
Formula
0to +∞Range -∞ to +∞0 to 1
.01
.1
.5
.6
.9
.99
1:99
1:9
1:1
3:2
9:1
99:1
-4.59
-2.20
0
.41
2.20
4.59
Values
0.0101
0.11
1
1.5
9
99

14. Logistic RegressionTheory
Male Female Total
Pass 45 25 70
Fail 5 25 30
Total 50 50 100
Male Female Total
Pass 45[.9]
Pass/Male
25 [.5]
Pass/Female
70 (.7)
Fail 5 [.1]
Fail/Male
25 [.5]
Fail/Female
30 (.3)
Total 50 (.5) 50 (.5) 100 (1)
ContingencyTable
ContingencyTable
with Conditional
Probabilities [ ]
Males have more
chances of passing

15. Male Female Total
Pass 45 25 70
Fail 5 25 30
Total 50 50 100
Odd Ratio
Male Female Total
Pass 45:5 25:25 70:30
Fail 5:45 25:25 30:70
Total 50 50 100
ContingencyTable
Odd Ratio
Males Have Better
Odd Ratio
Male Female Total
Pass 9:1 1:1 7:3
Fail 1:9 1:1 3:7
Total 50 50 100
Simplified Odd
Ratio
Male’s
Odd of
Passing
Female’s
Odd of
Passing

16. Male Female Total
Pass 9 1 2.33
Fail .111 1 .433
Total 50 50 100
Odd Ratio in
fraction
Relative Odd RatioRatio of Two
Odd Ratios
9/1 = 9

17. We are interested in the relationship between unemployment & Ethnic
Group for a sample of 18 years old.The following data is available
Ethnic Groups
White Black Total
1700 40 1740
112 8 120
1812 48 1860
Calculate
1. Conditional Probability of Being unemployed given each ethnic
Group
2. Odd ratio of being unemployed for both the Ethnic Groups
3. Simplified Odd ratios and Odd Ratios in numbers
4. Relative Odd Ratios

18. Conditional Probability for being Unemployed given each ethnic Group
Ethnic Groups
White Black Total
1700 40 1740
112 8 120
1812 48 1860
Ethnic Groups
White Black Total
1700/1812 40/48 1740
112/1812 8/48 120
1812/1812 48/48 1860

19. Ethnic Groups
White Black Total
.94 .83 1740
.06 .17 120
1 1 1860
Conditional Probability for being Unemployed given each ethnic Group

20. Odd Ratio for being Unemployed for each ethnic Group
Ethnic Groups
White Black Total
1700 40 1740
112 8 120
1812 48 1860
Ethnic Groups
White Black Total
1700:112 40:8 1740
112:1700 8:40 120
1812 48 1860

21. Ethnic Groups
White Black Total
15.2 5 1740
.066 .2 120
1812 48 1860
Odd Ratio for being Unemployed for each ethnic Group
Ethnic Groups
White Black Total
1700:112 40:8 1740
112:1700 8:40 120
1812 48 1860

22. Relative Odd Ratio for being Unemployed forWhite and Black
Relative Odd Ratio =
Odd Ratio of One Group for
Being Unemployed
Odd Ratio of the other Group
for Being Unemployed
= 0.33 to 1 = 3 to 1&

23. Logistic Example Manually &
Through SPSS
Ethnic Groups
White Black Total
90 30 120
19 33 52
109 63 172

24. Ethnic Groups
White Black Total
90 30 120
19 33 52
109 63 172
Ethnic Groups
White Black Total
0.83 0.48 120 (.7)
0.17 0.52 52 (.3)
109 (.63) 63 (.37) 172 (1)
Frequency Data
Conditional
Probability

25. Ethnic Groups
White Black Total
90 30 120
19 33 52
109 63 172
Frequency Data
Ethnic Groups
White Black Total
90:19 30:33 120
19:90 33:30 52
109 63 172
Odd Ratio
Ethnic Groups
White Black Total
4.73 0.91 120
0.21 1.1 52
109 63 172
Odd Ratio in
Fraction

26. White Having
Behavioral Problem
Black Having
Behavioral Problem
Conditional
Probability
Odd Ratio, Fraction
Relative Odd Ratio
Ln of Odd Ratio
0.17 0.52
19:90 = 0.21 33:30 = 1.1
0.192 to 1 5.21 to 1
-1.561 0.095
Logistic Equation
Ln(Odd Ratio) = -1.56 +1.65X
X = 0,
LnOR = -1.56
X = 1,
LnOR = 0.095
X = 0,
OR = 0.21
X = 1, OR = 1.1
0.17 0.52

28. compare the fit of
two models. How
well a model fits as
compared to the other.
-2Logliklihood
Lower theValue
better the fit of
Alternative
Chi Square
Test
Base Model is
better
Alternative is
better
Table showing how many
observations have been
predicted correctly
Both Models are
same
Proposed is better
Larger difference
is better
P < 0.05
Diagnosis of LR
Classification
Table
Difference between
the Base Model and
Proposed Model
Higher the correct prediction
the better

29. Likelihood Ratio Test
Based On
it checks whether the fuller model is better than the
base model.
What is it?
Loglikelihood function= -2loglikelihood
Measures the discrepancy between the observed and
predicted values
Interpretation
loglikelihood
Lower the value the better

30. Wald Test
Based On
Squared ratio between b1 and Sb1 , (b1/Sb1)2What is it?
Chi Square distribution at 1 df
Interpretation Larger value is significant

31. Measure of the Proportion of Variance
Based On
Measure of the proportion of variation explainedWhat is it?
Comparison of log-liklihood of the base and proposed model
Measures Cox & Snell’s R2 Nagelkerke’s R2
Interpretation
The higher the better (Value is between 0 & 1)
Does not attain 1 for
the perfect model
Attains1 for the perfect
model

32. The Hosmer-Lemeshow Goodness-of-Fit Test
Based On
What is it?
Interpretation Significant means the fit is bad

33. Interpreting the Logistic ModelModel
With one unit
increase in x
log(OR) of the
success will
increase by 1.3
units on average
Interpretation
Logit Odd Ratio Probability
With one unit
increase in x OR of
success will
increase by e1.3
units or by 3.67
units.
It gives the
probability of
success for a
particular value of x

34. Conducting Logistic Regression Using SPSS

35. Data Codes

38. Interpreting the Logistic ModelModelInterpretation
Logit
• Log of Odd ratio of being unemployed is -1.6 for the white
• Log of Odd Ratio of being unemployed decreases by 1.1 for
the Black

39. Interpreting the Logistic ModelModelInterpretation
Odd Ratio
• Odd ratio of being unemployed is 0.2 for the white
• Odd Ratio of being unemployed is 0.61
= 0.20
= 0.061

40. Logistic Regression with
Quantitative IndependentVariable
 We want to determine whether marks of
the students really determine the result
of the studetns

41. Logistic Regression

42. Logistic Regression

43. Logistic Regression

44. Logistic Regression