module 11

Question 1

logistic regression model

Answer 1

predict a categorical response variable w 2 levels

Question 2

simple logistic regression model equation

Answer 2

phat (probability) = 1/1+e^-(intercept + slopeexplanatory variable)
odds = phat/1-phat = e^(intercept + slopeexplanatory variable)
log odds = log(phat/ 1-phat)

Question 3

intercept interpretation

Answer 3

“We predict the odds of INCLUDE ALL CHARACTERISITCS FROM VARIABLE of being SUCCESSFUL are NUMBER”
Interpret e^intercept: the baseline odds

Question 4

Numerical Explanatory Variable Slope interpretation

Answer 4

“All else held equal if we were to increase the VARIABLE by 1, then we would expect the odds of SUCCESS to increase by a multiplicative factor of NUMBER on average.”
Interpret e^slope: odds multiplier of the explanatory variable

Question 5

Indicator variable slope interpretation

Answer 5

“All else held equal we expect that the odds INTERACTION TERM INCLUDED is SUCCESSto be a multiple of ODDS RATIO times higher than the odds BASELINE LEVEL is SUCCESS, on average.”

Need to calculate the log of the ratio of these 2 odds
log(oddyes/oddno) = log(oddsyes) - log(oddsno)
Convert back to get odds ratio

Question 6

Pseudo R^2

Answer 6

R^2 = 1 - LLF_full/LLF_null

Question 7

LLF_full

Answer 7

The highest possible log likelihood function value that we could achieve with intercept and slope
LF_full = 1, so LLF_full = 0 ideally bc ln(1) = 0 and LLF_full is log(LF_full)
The closer to 0, the better the fit for the training set

Question 8

Classifier model

Answer 8

set of rules that decide which of a set categories an observation belongs to, on the basis of training set of data containing observations whose category membership is known

Question 9

Predictive positive

Answer 9

True positive: observation predicted to be positive is actually positive
False positive: observation predicted to be positive is actually negative

Question 10

Predictive negative

Answer 10

True negative: observation predicted to be negative is actually negative
False negative: observation predicted to be negative is actually positive

Question 11

Confusion matrix

Answer 11

Predicted on top and actual on side

Question 12

Sensitivity rate

Answer 12

(true positive rate): TP/TP+FN

Question 13

Specificity rate

Answer 13

(true negative rate): TN/TN+FP

Question 14

assumption for log

Answer 14

Response variable needs to be a categorical variable with 2 possible outcomes
The relationship between the log odds of success and the combination of Xs should be linear
The observations need to be independent (inference)
No multicollinearity between the x variables (slope interpretability)
The sample size is large enough that to support the normal approximation
No strong outliers or influential points (inference)