interpret R Output – Statistic

interpret R Output – Statistic

The phenomenon of repealing criminal offenses is called recidivism.A study was conductedamong a sample of prisoners at a correctional facility in Baltimore to predict recidivism on thebasis of key demographic variables. The categorical dependent variable is Repeat(coded as 1 ifa prisoner has previously been convicted of a crime, and 0 if this is the first offense). Theindependent variables are Age (in years), Marred(marital status coded as 1 if married andliving with spouse at the time of the offense), and Education(number of years).Table 1 depicts the output from running a logistic regression model with all predictors using60% of the data as training data.(a) Suppose a particular prisoner is 42 years of age, notmarried and has had 7 years of education.What is the predicted probability that this prisoner has previously been convicted?Clearly show all calculations.Assuming a cutoff of 0.5, should this individual be classified as a repeat offender or not?(b) Provide an interpretation of the coefficient of Married.(c) Compute the accuracy of the classifier (Hint: based on the result of the validation data).(d) How many false positives are there in the validation data scoring?

see the whole Q in the attachment

The phenomenon of repealing criminal offenses is called recidivism. A study was conducted
among a sample of prisoners at a correctional facility in Baltimore to predict recidivism on the
basis of key demographic variables. The categorical dependent variable is Repeat (coded as 1 if
a prisoner has previously been convicted of a crime, and 0 if this is the first offense). The
independent variables are Age (in years), Marred (marital status coded as 1 if married and
living with spouse at the time of the offense), and Education (number of years).

Table 1 depicts the output from running a logistic regression model with all predictors using
60% of the data as training data.

(a) Suppose a particular prisoner is 42 years of age, not married and has had 7 years of education.

What is the predicted probability that this prisoner has previously been convicted?
Clearly show all calculations.
.
.
Assuming a cutoff of 0.5, should this individual be classified as a repeat offender or not?
(b) Provide an interpretation of the coefficient of Married.
(c) Compute the accuracy of the classifier (Hint: based on the result of the validation data).
(d) How many false positives are there in the validation data scoring?
Table 1: Output for the Question
Logistic Regression Output
## call:
## glm(formula = Repeat – Age + Married + Education, family = “binomial”, # data = train)
##
## Deviance Residuals:
##
Min
10. Median
30
Max
## -2.0460 -0.6011 -0.2992 0.5266 1.7443 ##
## Coefficients:
##
## (Intercept)
## Age
## Married
## Education
Estimate Std.
7.02980
-0.07742
-1.46957
-0.53501
Error z value pr(>IZI)
1.36894 5.135 2.82e-07 ***
0.02042 -3.792
0.00015 ***
0.46804 -3.140 0.00169 **
0.11920 -4.488 7.18e-06 ***
## –
## signif. codes: O ‘***’ 0.001 ***1 0.01 ‘*’ 0.05 ‘.’ 0.1″ 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 186.52 on 149 degrees of freedom
## Residual deviance: 124.55 on 146 degrees of freedom
## AIC: 132.55
##
## Number of Fisher Scoring iterations: 5
Training Data Scoring
##
Predicted
## Actual First Repeat
##
##
First
Repeat
90
22
13
25
Validation Data Scoring
##
Predicted
## Actual First Repeat
##
##
First
Repeat
62
12
13
13