For Exercises 1– 8, use the data in the table, which shows the average annual salaries (both in thousands of dollars) for public school counselors and public school librarians in the United States for 12 years.
Counselors, x
|
Librarians, y
|
48.2
|
46.7
|
50.0
|
49.0
|
50.0
|
48.7
|
51.7
|
49.6
|
52.3
|
50.4
|
52.5
|
50.7
|
53.7
|
53.3
|
55.9
|
54.9
|
57.6
|
56.9
|
58.8
|
58.0
|
60.1
|
59.5
|
60.2
|
59.1
|
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 and interpret the result.
3. Test the significance of the correlation coefficient r that you found in Exercise 2. Use a = 0.01.
4. Find the equation of the regression line for the data. Draw the regression line on the scatter plot that you constructed in Exercise 1.
5. Use the regression equation that you found in Exercise 4 to predict the average annual salary of public school librarians when the average annual salary of public school counselors is $59,500.
6. Find the coefficient of determination r2 and interpret the result.
7. Find the standard error of estimate se and interpret the result.
8. Construct a 99% prediction interval for the average annual salary of public school librarians when the average annual salary of public school counselors is $55,250. Interpret the results.