## Transcribed Text

For Exercises 1–8, refer to the data in the following table. The table lists the
personal income and outlays (both in trillions of dollars) for Americans for 11
recent years. (Source: U.S. Commerce Department, Bureau of Economic
Analysis)
Personal
income, x
Personal
outlays, y
4.5 3.7
4.9 4.0
5.0 4.1
5.3 4.3
5.6 4.6
5.9 4.8
6.2 5.1
6.5 5.4
7.0 5.7
7.4 6.1
7.8 6.5
1. Construct a scatter plot for 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
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. (Source: U.S. National Agricultural Statistics Service)
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

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction
of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.