10. A hospital is using a Poisson regression model (a type of GLM) to predict the number of emergency room visits per week based on patient age and medical history. The model is given by:
- Log(λ) =2.5-0.03Age+0.5condition where λ is the expected number of visits per week, Age is the patient’s age, and condition is a binary variable (1 if the patient has a chronic condition, 0 otherwise). Interpret the coefficients of Age and condition.
- What is the expected number of visits per week for a 60-year-old patient with a chronic condition?
- How would the expected number of visits change if the patient did not have a chronic condition?
PROGRAM:
import numpy as np
# Given Poisson regression coefficients
intercept = 2.5
coef_age = -0.03
coef_condition = 0.5
# Patient information
age = 60
condition = 1 # 1 if patient has chronic condition, 0 otherwise
# Calculate log(lambda)
log_lambda = intercept + coef_age * age + coef_condition * condition
# Convert to expected number of visits
expected_visits = np.exp(log_lambda)
print(f"Expected number of visits (with chronic condition): {expected_visits:.2f}")
# If patient does NOT have chronic condition
condition = 0
log_lambda_no_condition = intercept + coef_age * age + coef_condition * condition
expected_visits_no_condition = np.exp(log_lambda_no_condition)
print(f"Expected number of visits (without chronic condition): {expected_visits_no_condition:.2f}")OUTPUT:
Expected number of visits (with chronic condition): 3.32
Expected number of visits (without chronic condition): 2.01