A sociologist estimates the regression relating Poverty (y) to Education (x1). The estimated regression equation is:
= 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:
= 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?
What will be an ideal response?
a. H0: ?2 = ?3 = 0; HA: At least one ?j ? 0
b. F(2,35) = 26.83
c. Using the F table, the critical value approximately is F0.05,(2,35) ? 3.32
d. Because 26.83 > 3.32, we reject the null hypothesis and conclude that Median Income and the Mortality Rate are jointly significant in explaining Poverty.
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