Question

19. 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.

	df	SS	MS	F
Regression	3	417.3	139.1	94.6
Residual	47	69.1	1.47
Total	50	486.4
	Coefficients	Standard Error	t-stat	p-value
Intercept	60.3	4.8	12.47	1.65E-16
Education	−0.43	0.05	−7.78	5.45E-10
Income	−0.20	0.03	−7.75	6.02E-10
Morality	0.08	0.17	0.47	0.6438

The coefficient of determination indicates that ________.

Multiple Choice

• 86% of the variation in the poverty rate is explained by the sample regression equation.

• 14% of the variation in median incomes is explained by the sample regression equation.

• 14% of the variation in the poverty rate is explained by the regression model.

• 86% of the variation in median incomes is explained by the sample regression equation.

Answer 1

The coefficient of determination

86% of the variation in the poverty rate is explained by the sample regression equation.