Question

An insurance company has examined a random sample of 190 automobile accident claims for fraud. A logistic regression model is fitted to this data with the dependent variable being coded as one for a case that was fraudulent, and as zero otherwise. The five independent (predictor) variables included in the model are: – i . CityCode : =1 if the claimant lived in a large city, =0 otherwise; – ii. SexCode :=1 for males, =0 for females; – iii. Age in years; – iv. FaultCode :=1 if the fault in the accident was that of the policy holder, =0 otherwise; – v. Deductible Amount (in dollars). The model estimate for the logarithm of the odds of fraud is: 53.119 - 0.081×CityCode + 0.367× SexCode + 0.060×Age - 1.738× FaultCode - 0.142×Deductible Amount Situation: The insurance company has a claim by a male policyholder ages 30 years, who lives in a large city, has a deductible of $400 and who was not at fault in thr accident, Question: Calculate the odds, probability, and logit of fraud for this situation. Probability of Fraud Logit of Fraud Odds of Fraud Probability of "No Fraud"

A. o.168
B. -1.595
C. 0.203
D. 0.832

Answer 1

- Logarithms of the odds of fraud = -1.595 (option B)

- Odds of fraud = 0.02541

- Probability of fraud = 0.0248

- Probability of no fraud = 0.9752

Explanation:

The model estimate for the logarithm of the odds of fraud is: 53.119 - 0.081×CityCode + 0.367× SexCode + 0.060×Age - 1.738× FaultCode - 0.142×Deductible

The five independent (predictor) variables included in the model are:

– i . CityCode : =1 if the claimant lived in a large city, =0 otherwise;

– ii. SexCode :=1 for males, =0 for females;

– iii. Age in years;

– iv. FaultCode :=1 if the fault in the accident was that of the policy holder, =0 otherwise;

– v. Deductible Amount (in dollars)

So, the insurance company has a claim by a male policyholder ages 30 years, who lives in a large city, has a deductible of $400 and who was not at fault in thr accident,

Extracting the variables from this information

- Citycode = 1 (since the policyholder lives in a large city)

- Sexcode = 1 (since the policyholder is a male)

- Age in years = 30

- Faultcode = 0 (since the policyholder wasn't at fault for the accident)

- Deductible Amount in dollars = 400

Logarithms of the odds of fraud

= 53.119 - 0.081×CityCode + 0.367× SexCode + 0.060×Age - 1.738× FaultCode - 0.142×Deductible

Slotting in the variables

Logarithms of the odds of fraud

= 53.119 - (0.081×1) + (0.367× 1) + (0.060×30) - (1.738×0) - (0.142×400)

= 53.119 - 0.081 + 0.367 + 1.8 - 0 - 56.8

= -1.595

Logarithms of the odds of fraud = -1.595

Odds of fraud = Antilog (-1.595) = 0.0254097270555 = 0.02541

Probability of fraud = (odds)/(1 + odds)

= (0.02541/1.02541) = 0.0248

Probability of no fraud = 1 - (Probability of fraud)

= 1 - 0.0248 = 0.9752

Hope this Helps!!!