Multiple regression analysis was used to study how an individual's income (Y in thousands of dollars) is influenced by age (X1 in years), level of education (X2 ranging from 1 to 5), and the person's gender (X3 where 0 =female and 1=male). The following is a partial result of computer output that was used on a sample of 20 individuals. Present the estimated regression equation and compute the coefficient of determination. Explain it. Use the t test to determine the significance of each independent variable. Let α = 0.05. (For each test, give the null and alternative hypotheses, test statistic, and conclusion.) Use the F test to determine whether or not the regression model is significant. Let α = 0.05. (For the test, give the null and alternative hypotheses, test statistic, and conclusion.)
Multiple
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Present the estimated regression equation and compute the coefficient of determination. Explain it.
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Use the t test to determine the significance of each independent variable. Let α = 0.05. (For each test, give the null and alternative hypotheses, test statistic, and conclusion.)
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Use the F test to determine whether or not the regression model is significant. Let α = 0.05. (For the test, give the null and alternative hypotheses, test statistic, and conclusion.)
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Does the estimated regression equation provide a good fit for the observed data? Explain it.
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Suppose a new person with X1=40, X2=4, X3=0. Use the estimated regression equation in part (a) to estimate the new person’s income.
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