1) A consulting firm used a random sample of 12 CFOs (Chief Financial Officers) of large businesses to examine the relationship (if any) between salary and years of service in the firm.
a. Make a scatter plot and describe it. What general trends, if any, do you notice in the data?
b. Calculate a correlation coefficient and interpret it. How would you describe the direction and strength of the correlation?
| Years (x) | Salary (y),
in thousands |
| 1 | 220 |
| 11 | 180 |
| 4 | 190 |
| 8 | 180 |
| 18 | 150 |
| 12 | 145 |
| 6 | 250 |
| 15 | 160 |
| 18 | 130 |
| 5 | 185 |
| 6 | 180 |
| 5 | 165 |
2) Answer the questions below using the following Forbes data set.
Forbes 500 Random Subsample ($, millions)
Assets Sales Market Net Cash
Value Profit Flow
1,034.00 1,510.00 697.00 82.60 126.50
956.00 785.00 1,271.00 89.00 191.20
1,890.00 2,533.00 1,783.00 176.00 267.00
1,133.00 532.00 752.00 82.30 137.10
11,682.00 3,790.00 4,149.00 413.50 806.80
6,080.00 635.00 291.00 18.10 35.20
31,044.00 3,296.00 2,705.00 337.30 425.50
5,878.00 3,204.00 2,100.00 145.80 380.00
1,721.00 981.00 1,573.00 172.60 326.60
2,135.00 2,268.00 2,634.00 247.20 55.50
- Calculate a correlation matrix using the Forbes 500 dataset to find the correlation coefficient for each pair of variables in the table above. Write the matrix in table format. (Hint: You will calculate 10 correlation coefficients).
- Determine which variables have a significant linear relationship. Use the following figure to help describe the relationships:
-1.00 perfect negative correlation, -.50 moderate negative correlation, .50 is moderate correlation, 1.00 perfect positive correlation.
- Select two of the variables from the list above that you believe exhibit a strong linear relationship and have a cause-effect type of relationship. Designate the independent and dependent variable and run a regression analysis. What is the least squares regression equation? What can you conclude from the findings? What does the regression equation tell you about incremental changes in the independent variable and its effects on the dependent variable?
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