1. A consumer organization verified the area heated (in square feet) by 20 different electric space heaters with different wattages. The results are shown below, and theExcel data file can be accessed through the link in the "Required Textbook Reading".
| Heater |
Wattage |
Area |
Heater |
Wattage |
Area |
| 1 |
1,500 |
205 |
11 |
1,250 |
116 |
| 2 |
750 |
70 |
12 |
500 |
72 |
| 3 |
1.5 |
199 |
13 |
500 |
82 |
| 4 |
1.25 |
151 |
14 |
1,500 |
206 |
| 5 |
1.25 |
181 |
15 |
2,000 |
245 |
| 6 |
1250 |
217 |
16 |
1,500 |
219 |
| 7 |
1,000 |
94 |
17 |
750 |
63 |
| 8 |
2 |
298 |
18 |
1,500 |
200 |
| 9 |
1 |
135 |
19 |
1,250 |
151 |
| 10 |
1,500 |
211 |
20 |
500 |
44 |
Use the Regression tool in Excel's Data Analysis to answer the following questions.
Copy & paste the regression analysis output generated by Excel in the space below.
a. Write out the estimated regression equation for heating area based on wattage.
b. What does the value of the regression coefficient "b" tell us in this situation?
c. Conduct a test of hypothesis to determine if it might be possible that the population slope is equal to 0.17. Use the information provided by Excel to help you conduct the test at the .10 significance level.
d. What is the p-value? Does it support your conclusion regarding the null hypothesis? Explain.
2. Which of the following is not true regarding thestandard error of estimate: (circle as many as you think are false)
a. It is a measure of the variation around the regression line
b. It cannot be negative
c. It is in the same units as the independent variable
d. It approaches zero as the correlation coefficient approaches minus one
3. The following table shows the mean annual percent return on capital (profitability) and the mean annual percentage sales growth for eight aerospace and defense companies.
|
Company
|
Profitability |
Growth |
|
Alliant Techsystems
|
23.1
|
8.0
|
|
Boeing
|
13.2
|
15.6
|
|
General Dynamics
|
24.2
|
31.2
|
|
Honeywell
|
11.1
|
2.5
|
|
L-3 Communications
|
10.1
|
35.4
|
|
Northrop Grumman
|
10.8
|
6.0
|
|
Rockwell Collins
|
27.3
|
8.7
|
|
United Technologies
|
20.1
|
3.2
|
a. Let profitability be the dependent variable and growth be the independent variable. Create a scatter diagram with Excel. Copy & paste the diagram in the space below. Label both axis in your diagram.
b. Write out the estimated regression equation _________________________________
c. Use Excel to determine the value of the sample correlation coefficient _____________
d. Conduct a test of hypothesis to determine if it is reasonable to conclude that the population correlation is not equal to zero. State your null and alternative hypothesis, the decision rule (including critical value), compute the test statistic and make a decision. Use the .01 significance level.
e. Determine the residual for each observation (using software such as Excel is the most efficient way to do this). Which company has the largest residual and what is that residual?
4. Which of the following indicate a stronger correlation than -0.54? Circle all correct answers.
0.67 b. -0.89 c. 0.32 c. 0.00
5. Given the following sample observations,determine the summary sample statistics (mean of x and y, and standard deviation of x and y) using Excel.
|
x
|
6
|
10
|
14
|
19
|
21
|
|
y
|
5
|
3
|
7
|
8
|
12
|
a. Manually(not using computer software) compute the sample correlation coefficient, showing your work below.
b. Manually compute the estimates of the regression coefficients and write out the estimated regression equation. Show your work below.
6. Suppose we were interested in knowing if there was a relationship between total team salary and the performance of teams (number of wins) in the National Football League (NFL). Also suppose that a linear regression model predicting Wins based on Salary ($M) for all teams in the league was determined to be: y ^ = 1.783 + 0.062x
a. What does the y-intercept mean in this situation? Is it meaningful? Explain.
b. If one team spends $10 million more than another team on salary, how many more games on average would we predict them to win?
c. If a team spent $50 million on salaries and won 8 games, would they have done better or worse than predicted? Explain.