Statistics Solutions

[All Steps] Use the data in the table, which shows the personal income and outlays (both in trillions of dollars) for Americans for 11 recent years. Personal

Question: Use the data in the table, which shows the personal income and outlays (both in trillions of dollars) for Americans for 11 recent years.

Personal income, x Personal outlays, y
5.6
5.8
6.2
6.5
6.9
7.4
7.8
8.4
8.7
8.9
9.2 		4.6
4.9
5.2
5.5
5.8
6.1
6.5
7.0
7.3
7.7
8.0

The equation used to predict sunflower yield (in pounds) is

\[\hat{y}=1257\,-\,1.34{{x}_{1}}\,+\,1.41{{x}_{2}}\]

Where \({{x}_{1}}\) is the number of acres planted (in thousands) and \({{x}_{2}}\) is the number of acres harvested (in thousands). Use the regression equation to predict the y- values for the given values of the independent variables listed below. Then determine which variable has a greater influence on the value of y.

\[\begin{aligned} & (a)\,\,\,{{x}_{1}}\,=\,2103,\,\,\,{{x}_{2}}\,=\,2037 \\ & (b)\,\,\,{{x}_{1}}\,=\,3387,\,\,\,{{x}_{2}}\,=\,3009 \\ & (c)\,\,\,{{x}_{1}}\,=\,2185,\,\,\,{{x}_{2}}\,=1980 \\ & (d)\,\,\,{{x}_{1}}\,=\,3485,\,\,\,{{x}_{2}}\,=\,3404 \\ \end{aligned}\]

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