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A Sociologist Estimates the Regression Relating Poverty (Y) to Education

Question 50

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A sociologist estimates the regression relating Poverty (y) to Education (x1). The estimated regression equation is: A sociologist estimates the regression relating Poverty (y) to Education (x<sub>1</sub>). The estimated regression equation is: = 71.68 - 0.69x<sub>1</sub>; n = 39; SSE = 152. In an attempt to improve the results, he adds two more explanatory variables: Median Income (x<sub>2</sub>, in $1,000s) and the Mortality Rate (x<sub>3</sub>, per 1,000 residents). The estimated regression equation is: = 59.80 - 0.44x<sub>1</sub>- 0.18x<sub>2</sub> + 0.17x<sub>3</sub>; n = 39; SSE = 60. A) Formulate the hypotheses to determine whether Median Income and the Mortality Rate are jointly significant in explaining Poverty. B) Calculate the value of the test statistic. C) At the 5% significance level, find the approximate value of the critical value(s). D) What is the conclusion to the test? = 71.68 - 0.69x1; n = 39; SSE = 152.
In an attempt to improve the results, he adds two more explanatory variables: Median Income (x2, in $1,000s) and the Mortality Rate (x3, per 1,000 residents). The estimated regression equation is: A sociologist estimates the regression relating Poverty (y) to Education (x<sub>1</sub>). The estimated regression equation is: = 71.68 - 0.69x<sub>1</sub>; n = 39; SSE = 152. In an attempt to improve the results, he adds two more explanatory variables: Median Income (x<sub>2</sub>, in $1,000s) and the Mortality Rate (x<sub>3</sub>, per 1,000 residents). The estimated regression equation is: = 59.80 - 0.44x<sub>1</sub>- 0.18x<sub>2</sub> + 0.17x<sub>3</sub>; n = 39; SSE = 60. A) Formulate the hypotheses to determine whether Median Income and the Mortality Rate are jointly significant in explaining Poverty. B) Calculate the value of the test statistic. C) At the 5% significance level, find the approximate value of the critical value(s). D) What is the conclusion to the test? = 59.80 - 0.44x1- 0.18x2 + 0.17x3; n = 39; SSE = 60.
A) Formulate the hypotheses to determine whether Median Income and the Mortality Rate are jointly significant in explaining Poverty.
B) Calculate the value of the test statistic.
C) At the 5% significance level, find the approximate value of the critical value(s).
D) What is the conclusion to the test?

Correct Answer:

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a. H0: β2 = β3 = 0; HA: At least one βj ≠ 0
b....

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