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Binary Logistic Regression Analysis

1. Logistic Regression

When the dependent variable is binary coded (eg. success vs failure), using simple linear regression to model the outcome variable may not be suitable. Instead of using linear regression, one can consider binary logistic regression instead.

2. The general notation of a logistic regression model

ln(p/q) = B0 + B1x + u

Where,

  • ln(p/q) is the dependent variable
  • x is the independent variable
  • B0 is the intercept
  • B1 is the slope

3. Parameter estimation in logistic regression

Unlike linear regression, ordinary least square method may not be appropriate in determining the parameters in the logistc regression. For logistic regression, a likelihood function can be form and the parameters can be determined through maximum likelihood method and solve for the parameters using gradient descent.

Question

Determine the cofficient for the independent variable for the following datasets.

 

Question 1

 

DV1 IV1
0 6
1 7
1 2
0 8
1 6
0 2
1 3
0 8
1 5
0 2
0 8
1 10
1 2
0 5
0 8
0 4
1 8
1 7
1 1
1 8
1 2

Question 2

 

DV2 IV2
1 10
0 7
1 8
0 9
1 1
0 8
0 8
0 9
0 5
0 1
0 8
1 4
0 1
1 10
1 2
0 8
0 4
0 1
1 1
1 10
1 4

 

Question 3

 

DV3 IV3
0 2
1 6
0 2
1 8
1 5
1 5
1 9
0 5
1 6
0 10
0 5
1 8
0 9
1 9
1 8
1 4
1 3
1 8
0 4
1 3
1 3

 

Question 4

 

DV4 IV4
0 6
1 3
0 9
1 4
1 9
0 9
1 10
0 4
1 5
1 3
1 1
1 7
1 9
0 9
1 4
1 1
1 10
0 6
0 8
0 2
1 9

 

Question 5

 

DV5 IV5
1 1
1 4
0 4
0 3
0 9
0 7
0 5
0 3
1 1
0 6
0 6
0 5
1 7
0 10
0 8
0 3
1 6
0 4
1 7
0 9
1 7

 

Question 6

 

DV6 IV6
0 3
0 7
1 7
1 8
1 5
1 1
1 2
1 5
1 4
0 6
1 9
0 2
0 9
1 8
1 4
1 7
0 9
1 9
0 6
1 5
1 6

 

Answer

  1. -0.0809
  2. -0.0171
  3. 0.1301
  4. -0.0977
  5. -0.195
  6. -0.0491

Notes: There are other useful information can be determined when performing logistic regression analysis such as the Nagelkerke R-squared.

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