1. Logistic Regression
--> used to describe the relationship between
Discrete Y
Continuous X
Y --> usually dichotomous or binary

2. Examples of dichotomous Y variable
Presence - Absence
Alive - Dead
Male - Female
Red - Green
Scored as 0’s and 1’s

7. Y = (X)

10. #Cigs

21. Correlation Analysis Like Regression Unlike Regression
Testing for linear relationship
Unlike Regression
Variables not assumed to be functionally dependent
No Causality

22. The Correlation Coefficient (r)
- = negative association
+ = positive association
r = 0  no linear association

23. Example: Relationship between wing and tail lengths
Wing Length (cm) (x)
Tail Length (cm) (y)
10.4
7.4
10.8
7.6
11.1
7.9
10.2
7.2
10.3
7.1
10.7
10.5
7.8
11.2
7.7
10.6
11.4
8.3
Correlation Coefficient = r = 0.870

24. Hypothesis Testing with Correlation Coefficients
r is estimate of population parameter ρ
Test using Student’s t
Standard Error of r

25. Using Bird Example Standard error of r
Therefore reject H0 there is a linear association between wing and tail lengths

26. Instead of t Can use F where:
Can use Critical Values Table of the Correlation Coefficient
Gives minimum r-value that is significant for a given degrees of freedom

27. Assumptions X and Y have come at random from normal populations And
X values at each Y have come at random from normal populations
Effect of normality most obvious when there is strong association
No effect of sample size

28. Spearman Rank Correlation (rs)
Use when data is from a non-normal population
Not as powerful a test if data is normal
Each measurement is ranked (i.e. non-parametric)
Use critical values table to assess significance
di = rank of Xi – rank of Yi

29. Correction for Tied Data
Assign average rank for tied data
E.g. (3 + 4)/2 = 3.5 or ( )/3 = 5
Correction for Tied Data
Where:

30. Example Using Bird Data
Rank of X Y
Rank of Y di
di2
10.4 4
7.4 5 -1 1
10.8
8.5
7.6 7
1.5
2.25
11.1 10
7.9 11
10.2
7.2
2.5
0.25
10.3 3 -2
7.1
0.5
10.7 2
10.5
6.25
7.8
9.5
11.2
7.7 8 9
10.6 6
-3.5
12.25
11.4 12
8.3
To test H0: ρs = 0; HA: ρs ≠ 0
(rs)0.05(2),12 = 0.587
Therefore Reject Null

31. With Correction for Ties
Among X’s there are two of 10.2 and two of 10.8
Among Y’s there are two of 7.2, three of 7.4, and two of 7.8
Therefore