According to the Center for Disease Control and Prevention, life expectancy at age 65 in America is about 18.7 years. Medical researchers have argued that while excessive drinking is detrimental to health, drinking a little alcohol every day, especially wine, may be associated with an increase in life expectancy. Others have also linked longevity with income and gender. Data were collected related to the length of life after 65 (Life) were collected including the average income (in $1,000s) (Income), the average number of alcoholic drinks consumed per day (Drinks), and a dummy variable Woman which is 1 when the individual is a woman and 0 otherwise. The following model was created: Life = β₀ + β₁Income + β₂Drinks + β₃Woman + ε. Output corresponding to this model is shown below. Which of the following is the predicted life expectancy for a 65-year-old man with an income of $50,000 and a consumption of three drinks per day? A) 19.78 B) 16.58 C) 13.38 D) 18.70

Question

Quizplus · Accepted Answer

Using the coefficients from the output, we can plug in the values for Income (50) and Drinks (3) for a 65-year-old man who is not a woman:

Life = 27.08 + 0.51(50) - 0.21(3) + 0ε
Life = 27.08 + 25.50 - 0.63
Life = 51.95

However, we must remember that Life represents the number of years after age 65, so we must subtract 18.7 (the life expectancy for a 65-year-old per the CDC) to get the predicted life expectancy:

Predicted Life Expectancy = 51.95 - 18.7
Predicted Life Expectancy = 16.25

Therefore, the predicted life expectancy for a 65-year-old man with an income of $50,000 and a consumption of three drinks per day is approximately 16.25 years. The closest answer choice is B) 16.58.

According to the Center for Disease Control and Prevention, Life