Personal Income Analysis
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The table lists the personal income and outlays (both in trillions of dollars) for Americans for 11 recent years.
Personal income, x
4.5
4.9
5.0
5.3
5.6
5.9
6.2
6.5
7.0
7.4
7.8
Personal outlays, y
3.7
4.0
4.1
4.3
4.6
4.8
5.1
5.4
5.7
6.1
6.5
1. Construct a scatter plot for the data. Do the data appear to have a positive linear correlation, a negative linear correlation, or no linear correlation? Explain.
2. Calculate the correlation coefficient r. What can you conclude?
3. Test the level of significance of the correlation coefficient r . Use a = 0.05 .
4. Find the equation of the regression line for the data. Include the regression line in the scatter plot.
5. Use the regression line to predict the personal outlays when the personal income is 5.3 trillion dollars.
6. Find the coefficient of determination and interpret the results.
7. Find the standard error of estimate se and interpret the results.
8. Construct a 95% prediction interval for personal outlays when personal income is 6.4 trillion dollars. Interpret the results.
9. The equation used to predict sunflower yield (in pounds) is
y = 1257 - 1.34x1 + 1.41x2
where x1 is the number of acres planted (in thousands) and x2 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.
(a) x1 = 2103 , x2 = 2037
(b) x1 = 3387 , x2 = 3009
(c) x1 = 2185 , x2 = 1980
(d) x1 = 3485 , x2 = 3404
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Personal income analysis is examined.
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