A sociologist examines the relationship between the poverty rate and several socioeconomic factors. For the 50 states and the District of Columbia (n = 51), he collects data on the poverty rate (y, in %), the percent of the population with at least a high school education (x₁), median income (x₂, in $1000s), and the mortality rate per 1,000 residents (x₃). He estimates the following model as = β₀ + β₁Education + β₂Income + β₃Mortality + ε. The following ANOVA table shows a portion of the regression results. What is the poverty rate for a state where 85% of the population has at least a high school education, the median income is $50,000, and the mortality rate is 10 per 1,000 residents? A) 12.6% B) 14.6% C) 16.6% D) 18.6%

Question

Quizplus · Accepted Answer

Using the regression equation, we can estimate the poverty rate for a state with 85% high school education, $50,000 median income, and 10 mortality rate:
Poverty Rate = β0 + β1(Education) + β2(Income) + β3(Mortality) + ε
= 20.24 + (-0.44)(85) + (-0.16)(50) + (0.05)(10) + ε
= 14.62 + ε
Therefore, the predicted poverty rate is 14.62%, which corresponds to choice B.

A Sociologist Examines the Relationship Between the Poverty Rate and Several