STAT 164 - 3RD LE - CHAPTER 6.2

LOGISTIC REGRESSION

It is used to study the relationship between a categorical dependent variable and independent variables that can either be quantitative and/or categorical.

• Binary

• Multinomial

• Ordinal

Type of logistic regression is based on the nature of the dependent variable:

• ____________ (ex. dead or alive; success or failure; yes or no)

• ____________ (ex. Asia, Africa, America, or Europe)

• ____________ (ex. Life satisfaction level)

BINARY LOGISTIC REGRESSION

• It models a binary dependent variable using independent variables (that can either be continuous and/or categorical)

• The model computes the probability that the event of interest will occur as a function of the independent variables.

What is the formula for the following:

• Probability model form

• Odds model form

• Logit model form

Provide the following:

• Estimated LOGIT model

• Possible interpretations of the coefficients

• Test of Hypothesis, α = 10%, p-value: 0.0884

  • Ho (in words):

  • Ha (in words):

  • Decision:

  • Conclusion:

What is the probability of observing a wolf spider given that the grain size is equal to 0.4?

Confusion Matrix

________________ — a cross-tabulation of the actual and the predicted values. It helps us in assessing the accuracy of the model.

Sensitivity

MODEL EVALUATION

_____________ - the proportion of true positives or the proportion of cases correctly identified by the test as meeting a certain condition (e.g. in mammography testing, the proportion of patients with cancer who test positive).

Specificity

MODEL EVALUATION

________________ - the proportion of true negatives or the proportion of cases correctly identified by the test as not meeting a certain condition (e.g. in mammography testing, the proportion of patients without cancer who test negative).

Calculate the following:

• Overall Accuracy (%)

• Sensitivity (%)

• Specificity (%)

• False Negative Rate (%)

• False Positive Rate (%)

Provide the following:

• Estimated LOGIT model

• Possible interpretations of the coefficients
  

Test of Hypothesis - α = 5%

• Age, p-value: 0.0147

  • Conclusion:

• Gender, p-value: 0.0618

  • Conclusion:

Calculate the following:

• Overall Accuracy (%)

• Sensitivity (%)

• Specificity (%)

• False Negative (%)

• False Positive (%)

PROBIT REGRESSION MODEL

• Another model that has S-shaped curve

• The model transforms the probabilities to Z-scores from the standard normal distribution.

Probit Regression Model formula.

PROBIT REGRESSION MODEL

The model outputs left-tailed Z-scores which is then converted into cumulative probabilities using the Z-table.

Provide the estimated probit regression model and 

Also what solve for the effective level EL₅₀.