logistic regression. linear regression purchases vs. income
TRANSCRIPT
Logistic Regression
Linear Regression
Purchases vs. Income
R Graphical Parameters
Purchase Dataset
• Conceptually, if a person has greater income, the probability that he or she will purchase is greater than if the person has less income.
Categorical with a Linear Model
Residual vs .Fitted
Categorical Dependent Variable
Binary Data
Don’tPrefer
Log is better at representing the data
Logistic Regression
bXaY
YODDS
ˆ1
ˆlnln
19237.025.1 XeODDS
Percent Yes --> PNo 165 49%
Yes 170 51%335
Odds Ratio 51% 1.0349%
Log Odds Ratio (Logit)Const Beta
Ln (Odds) 1.25 0.92
Exp(Beta) = OddsExp(0.92) = 2.52
Odds * Exp(Beta) 2.59
Calculated% 72%
Original Percentage 51%
Delta 21%
The original classification table is put in here to get the Ns as well as to get the original percent among the respondents
The original percent is turned into a probability
The Average Odds is then multiplied by the Exp of the Beta.
Which is then turned back into a percentage
The original percentage is subtracted from the predicted percent to determine the change
~1:1 Ratio for getting a No or Yes
Logit ModelIncludes Log;So Need to
Convert to Odds
2.52 vs. 1.03
Odds = P / (1-P)Odds – (Odds*P) = POdds = P + Odds*POdds = P(1 + Odds)P = Odds / (1 + Odds)
Delta from the Average Odds
100%-72% = 28%
72% / 28% = 2.6
The Regression Beta is then converted to Odds.
Mathematics
Logistic Regression
Measure of Goodness• R^2 ranges from 0 to 1.0, and can be considered as
a percentage of variability. An R 2 of 1.0—or 100%—means that 100% of the variance in the dependent variable can be explained by variability in the independent variable or variables.
• We use the log likelihood as our criterion for the “best” coefficients.
• The closer to 0.0 a log likelihood:• the better the fit• the closer you’ve come to maximizing the estimate of
the likelihood.
• Probability of No Purchase: • Person who did not purchase has a 0 on the Purchased variable• Predicted probability of 2% that he will purchase
• Probability of Purchase: • Person who did purchase has a 1 on the Purchased variable• Predicted probability of 94% that this person will purchase
• The probabilities are of two different events: • No Purchase and Purchase• In the first case, it’s 98% that he doesn’t purchase, and he doesn’t.