Logistic Regression

Logistic Regression Report

Data, Method, and Model


Number of cases used in the analysis	756
Number of incomplete (omitted) cases	556
Link Function	logit
Model	Survived ~ Age +PClass

Response Information

Variable	Value	Count
Survived	Survived	313	(Event)
	Died	443
	Total	756

Parameter Estimates

Model formula: Survived ~ Age +PClass
Event = Survived
Reference Level(s): PClass (1st)

Term	Coefficient	Standard Error	Z-Value	P-Value
(Intercept)	2.0337	0.3069	6.627	3.425e-11
Age	-0.038504	0.006546	-5.882	4.045e-09
PClass (2nd)	-1.1458	0.2203	-5.202	1.97e-07
PClass (3rd)	-2.2315	0.229	-9.745	1.94e-22

Odds Ratios

Model formula: Survived ~ Age +PClass
Event = Survived
Reference Level(s): PClass (1st)

Term	Change	Odds Ratio	2.5% Lower CL	97.5% Upper CL
Age	1	0.9622	0.95	0.9747
PClass (2nd)		0.318	0.2065	0.4896
PClass (3rd)		0.1074	0.06854	0.1682

Measures of Model Fit

Model formula: Survived ~ Age +PClass
Event = Survived

Measure	Value	df
Deviance*	909.917	752
Null Deviance**	1025.57	755
Log Likelihood	-454.958	4
MSE (Brier Score)	0.206482
R-Squared	11.28%
Adj R-Squared	10.92%
AIC	917.917
BIC	936.429

* Deviance for the specified model.
** Deviance for the intercept-only model.

Goodness-of-Fit Tests

Test	DF	Chi-Square	P-Value
Deviance	752	909.917	6.295e-05
Pearson	752	764.977	0.3632
Hosmer-Lemeshow*	8	9.3605	0.3128

*Number of groups for the Hosmer-Lemeshow test = 10

Confusions Matrix

Event = Survived; Classification Cutoff = 0.5

Actual	Predicted Survived	Predicted Died	Total
Survived	158 (20.9%)	155 (20.5%)	313 (41.4%)
Died	93 (12.3%)	350 (46.3%)	443 (58.6%)
Total	251 (33.2%)	505 (66.8%)	756 (100%)

Confusion Matrix Graph

A graph of the confusion matrix. The classification cutoff is 0.5The y-axis is the predicted probabilities, and the x-axis is
the actual observed values of the response with the event beingSurvivedThe true positives are shown on the top left, true negatives are shown
in the bottom right, the false positives are shown on the top right
, and the false negatives are shown in the bottom left.

Density of Predicted Probabilities

A graph of the densities of predicted probabilities corresponding
to observed events and non-events. The x-axis depicts the probabilities and
the y-axis shows the density values. The event here isSurvivedand Thenon-event isDied

ROC Plot and Cost Function Plot

ROC and Cost Plots, AUC = 0.721
FP Cost = 1, FN Cost = 1, Optimal Cutoff = 0.53, Total Cost = 238for the ROC curve , ,
The x-axis is False Positive rate and it ranges from 0 to 1, ,
, the y-axis is the TRUE positive rate, and it ranges from 0 to 1.
For the cost function the x-axis is the classification cutoff and
the y-axis is the cost that ranges from 238 , , to , ,443