An insurance agent wants to identify which prospective customers are worth contacting to sell supplemental health insurance, such as coverage for critical illness, accidents, hospital insurance, etc.
Consider the following logistic regression model that uses hourly wage, an indicator for heart disease (coded 1 if the customer has heart disease and 0 if not), and the number of insurance policies that the customer already has, to explain the log-odds of purchasing supplemental health insurance:
Ln(odds of purchasing insurance) = 1.2752 + 0.0229*Hourly wage + 0.2321*Heart disease – 0.0275*number of policies
What is the estimated effect on the odds of purchasing the insurance policy if a customer’s hourly wage is 5 dollars lower than another customer with the same number of insurance policies given that both customers do not have heart disease?
The estimated odds of purchasing will be 20.47 percent lower.
The estimated odds of purchasing will be 10.82 percent lower.
The estimated odds of purchasing will be 5.65 percent higher.
The estimated odds of purchasing will be 14.74 percent higher.
To find the estimated effect on the odds of purchasing the insurance policy, we need to substitute the given information into the logistic regression model.
From the model, the coefficient for Hourly wage is 0.0229. This means that for every 1 unit increase in hourly wage, the odds of purchasing the insurance policy increase by 0.0229.
If a customer's hourly wage is 5 dollars lower than another customer with the same number of insurance policies, we need to substitute this information into the model.
So we have:
Hourly wage = -5 (since it's 5 dollars lower)
Heart disease = 0 (since both customers do not have heart disease)
Number of policies = same for both customers
Substituting these values into the model, we have:
Ln(odds of purchasing insurance) = 1.2752 + 0.0229*(-5) + 0.2321*0 - 0.0275*(number of policies)
Since we are only interested in the effect on the odds of purchasing, we don't need to calculate the specific log-odds value.
The coefficient for Hourly wage is -0.1145 (-5*0.0229), indicating that for every 1 unit decrease in hourly wage, the odds of purchasing the insurance policy decrease by 0.1145.
Therefore, the estimated odds of purchasing will be 11.45 percent lower if a customer's hourly wage is 5 dollars lower than another customer with the same number of insurance policies given that both customers do not have heart disease.
However, this answer is not provided in the answer choices.