A researcher analyzes the factors that may influence the poverty rate and estimates the following model: y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε,where y is the poverty rate (y,in %),x₁ is the percent of the population with at least a high school education,x₂ is the median income (in $1,000s),and x₃ is the mortality rate (per 1,000 residents).The researcher would like to construct interval estimates for y when x₁,x₂,and x₃ equal 85%,$50,000,and 10,respectively.The researcher estimates a modified model where poverty rate is the response variable and the explanatory variables are now defined as A portion of the regression results is shown in the accompanying table. a.According to the modified model,what is the point estimate for the poverty rate when x₁,x₂,and x₃ equal 85%,$50,000,and 10,respectively.
b.According to the modified model,what is a 95% confidence interval for the expected poverty rate when x₁,x₂,and x₃ equal 85%,$50,000,and 10,respectively? ? (Note that t_0.025,35 = 2.030. )
c.According to the modified model,what is a 95% prediction interval for the poverty rate when x₁,x₂,and x₃ equal 85%,$50,000,and 10,respectively? (Note that t_0.025,35 = 2.030. )

Question

A researcher analyzes the factors that may influence the poverty rate and estimates the following model: y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε,where y is the poverty rate (y,in %),x₁ is the percent of the population with at least a high school education,x₂ is the median income (in $1,000s),and x₃ is the mortality rate (per 1,000 residents).The researcher would like to construct interval estimates for y when x₁,x₂,and x₃ equal 85%,$50,000,and 10,respectively.The researcher estimates a modified model where poverty rate is the response variable and the explanatory variables are now defined as

A researcher analyzes the factors that may influence the poverty rate and estimates the following model: y = β<sub>0</sub> + β<sub>1</sub>x<sub>1</sub> + β<sub>2</sub>x<sub>2</sub> + β<sub>3</sub>x<sub>3</sub> + ε,where y is the poverty rate (y,in %),x<sub>1</sub> is the percent of the population with at least a high school education,x<sub>2</sub> is the median income (in $1,000s),and x<sub>3</sub> is the mortality rate (per 1,000 residents).The researcher would like to construct interval estimates for y when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively.The researcher estimates a modified model where poverty rate is the response variable and the explanatory variables are now defined as A portion of the regression results is shown in the accompanying table. a.According to the modified model,what is the point estimate for the poverty rate when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively. b.According to the modified model,what is a 95% confidence interval for the expected poverty rate when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively? ? (Note that t<sub>0.025,35</sub> = 2.030. ) c.According to the modified model,what is a 95% prediction interval for the poverty rate when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively? (Note that t<sub>0.025,35</sub> = 2.030. )

A portion of the regression results is shown in the accompanying table.

a.According to the modified model,what is the point estimate for the poverty rate when x₁,x₂,and x₃ equal 85%,$50,000,and 10,respectively.
b.According to the modified model,what is a 95% confidence interval for the expected poverty rate when x₁,x₂,and x₃ equal 85%,$50,000,and 10,respectively? ? (Note that t_0.025,35 = 2.030. )
c.According to the modified model,what is a 95% prediction interval for the poverty rate when x₁,x₂,and x₃ equal 85%,$50,000,and 10,respectively? (Note that t_0.025,35 = 2.030. )

Quizplus · Accepted Answer

The Answer of A researcher analyzes the factors that may influence the poverty rate and estimates the following model: y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε,where y is the poverty rate (y,in %),x₁ is the percent of the population with at least a high school education,x₂ is the median income (in $1,000s),and x₃ is the mortality rate (per 1,000 residents).The researcher would like to construct interval estimates for y when x₁,x₂,and x₃ equal 85%,$50,000,and 10,respectively.The researcher estimates a modified model where poverty rate is the response variable and the explanatory variables are now defined as A portion of the regression results is shown in the accompanying table. a.According to the modified model,what is the point estimate for the poverty rate when x₁,x₂,and x₃ equal 85%,$50,000,and 10,respectively. b.According to the modified model,what is a 95% confidence interval for the expected poverty rate when x₁,x₂,and x₃ equal 85%,$50,000,and 10,respectively? ? (Note that t_0.025,35 = 2.030. ) c.According to the modified model,what is a 95% prediction interval for the poverty rate when x₁,x₂,and x₃ equal 85%,$50,000,and 10,respectively? (Note that t_0.025,35 = 2.030. )

A Researcher Analyzes the Factors That May Influence the Poverty