# Correlation and regression: key informaiton

Use the data in the table, which shows 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

5.6 4.6

5.8 4.9

6.2 5.2

6.5 5.5

6.9 5.8

7.4 6.1

7.8 6.5

8.4 7.0

8.7 7.3

8.9 7.7

9.2 8.0

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 and interpret the results.

8. Construct a 95% prediction interval for personal outlays when personal income is 6.4 trillion dollars. Interpret the results.

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#### Solution Preview

Please see attached file:

For Exercises 1-8, use the data in the table, which shows 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

5.6 4.6 0.995917753

5.8 4.9

6.2 5.2

6.5 5.5

6.9 5.8

7.4 6.1

7.8 6.5

8.4 7.0

8.7 7.3

8.9 7.7

9.2 8.0

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.

The data appear to have a positive linear correlation as with an increase in personal income, personal outlays is increasing.

2. Calculate the correlation coefficient r. What can you conclude?

(X) ...

#### Solution Summary

A correlation and regression analysis has been carried out. A scatter plot for the data has been constructed. The correlation coefficient has been calculated and tested for significance. Equation of the regression line for the data has been calculated. The regression line has been used to make prediction. The coefficient of determination and the standard error of estimate have been calculated.