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 + β₁ Education + β₂ Income + β₃ Mortality + 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

From the model, 
Poverty rate = β0 + β1(Education) + β2(Income) + β3(Mortality) + ε
Substituting the given values:
Poverty rate = β0 + β1(85) + β2(50) + β3(10) + ε
From the ANOVA table, we can see that β1 = -0.240 and β2 = -0.064
Substituting these values:
Poverty rate = β0 - 0.240(85) - 0.064(50) + β3(10) + ε
We do not have information about the value of β0 or ε, but we do know that the poverty rate is the predicted value, so we can ignore them for this calculation. 
Thus, Poverty rate = -0.240(85) - 0.064(50) + β3(10) = -20.4 + 10β3
From the ANOVA table, we can see that β3 is not significant (p-value = 0.128), so we can assume that it is close to zero. 
Thus, Poverty rate ≈ -20.4 + 0 ≈ -20.4 
However, the poverty rate cannot be negative, so we take the absolute value of this result:
Poverty rate ≈ 20.4%
Therefore, the poverty rate for a state with 85% of the population having at least a high school education, median income of $50,000 and a mortality rate of 10 per 1,000 residents is 20.4%, which is closest to option B (14.6%).

A Sociologist Examines the Relationship Between the Poverty Rate and Several