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 y = β₀ + β₁Education + β₂Income + β₃Mortality + ε. The following ANOVA table shows a portion of the regression results. The coefficient of determination indicates that ________. A) 14% of the variation in the poverty rate is explained by the regression model. B) 14% of the variation in median incomes is explained by the sample regression equation. C) 86% of the variation in the poverty rate is explained by the sample regression equation. D) 86% of the variation in median incomes is explained by the sample regression equation.

Question

Quizplus · Accepted Answer

The coefficient of determination (R-squared) reflects the proportion of the variation in the dependent variable (poverty rate) that is explained by the independent variables in the model. In this case, the ANOVA table shows that R-squared = 0.86, which means that 86% of the variation in poverty rate is explained by the model. Therefore, answer C is correct. Answers A, B, and D are incorrect because they refer to either the wrong dependent variable or the wrong proportion of variation explained.

A Sociologist Examines the Relationship Between the Poverty Rate and Several