Question 1. The F test is used in Analysis of Variance (ANOVA). When would a researcher use an ANOVA? Explain.
Question 2. What is the role of R square in regression analysis? How does R square differ from the adjusted R square? Explain.
3. Jacob Lee is a frequent traveler between Los Angekes and San Francisco. For the past month, he wrote dowh the flight times On three different airlines. The results are:
| Goust |
Jet Red |
Cloudtran |
| 51 |
50 |
52 |
| 51 |
53 |
55 |
| 52 |
52 |
60 |
| 42 |
62 |
64 |
| 51 |
53 |
61 |
| 57 |
49 |
49 |
| 47 |
50 |
49 |
| 47 |
49 |
|
| 50 |
58 |
|
| 60 |
54 |
|
| 54 |
51 |
|
| 49 |
49 |
|
| 48 |
49 |
|
| 48 |
50 |
|
a. Use the .05 significance level and the five-step hypothesis-testing process to check if ther,e is a difference in thesmean flight times among the three airlines.
b. Develbp a. 95% confidence interval for the difference In the means between Goust and Cloudtran.
4. Three assembly lines are used to produce a certain component for an airliner. To exam¬ine the production rate, a random sample of six hourly periods is chosen for each assem¬bly line and the number of components produced during these periods for each line is recorded. The output from a statistical software package is:
Summary
|
Groups
|
Count
|
Sum
|
Average
|
Variance
|
|
Line A
|
6
|
250
|
41.66667
|
0.266667
|
|
Line B
|
6
|
260
|
43.33333
|
0.666667
|
|
Line C
|
. 6
|
249
|
41.5
|
0.7
|
5. Refer to the Baseball 2010 data, which report information on the 30 Major League Base¬ball teams for the 2010 season. Let the number of games won be the dependent variable and the following variables be independent variables: team batting average, number of stolen bases, number of errors committed, team ERA, number of home runs, and whether the team plays in the American or the National League. Add a league code variable using 0 for the National League and 1 for the American League.
a. Use a statistical software package to determine the multiple regression equation. Dis-cuss each of the variables. For example, are you surprised that the regression coeffi-cient for ERA is negative? Is the number of wins affected by whether the team plays in the National or the American League?
b. Find the coefficient of determination for this set of independent variables.
c. Develop a correlation matrix. Which independent variables have strong or weak corre-lations with the dependent variable? Do you see any problems with multicollinearity?
d. Conduct a global test on the set of independent variables. Interpret.
e. Conduct a test of hypothesis on each of the independent variables. Would you con¬sider deleting any of the variables? If so, which ones?
f. Rerun the analysis until only significant net regression coefficients remain in the analy-sis. Identify these variables.
g. Develop a histogram of the residuals from the final regression equation developed in part (f). Is it reasonable to conclude that the normality assumption has been met?
h. Plot the residuals against the fitted values from the final regression equation developed in part (f). Plot the residuals on the vertical axis and the fitted values on the hori¬zontal axis.
6. A consumer analyst collected the following data on the screen sizes of popular LCD televisions sold recently at a larger retailer.
|
Manufacturer
|
Screen
|
Price
|
|
Sharp
|
46
|
$1473.00
|
|
Samsung
|
52
|
2300.00
|
|
Samsung
|
46
|
1790.00
|
|
Sony
|
40
|
1250.00
|
|
Sharp
|
42
|
1546.50
|
|
Samsung
|
46
|
1922.50
|
|
Samsung
|
40
|
1372.00
|
|
Sharp
|
37
|
1149.50
|
|
Sharp
|
46
|
2000.00
|
|
Sony
|
40
|
1444.50
|
|
Sony
|
52
|
2615.00
|
|
Samsung
|
32
|
747.50
|
|
Sharp
|
37
|
1314.50
|
|
Sharp
|
32
|
853.50
|
|
Sharp
|
52
|
2778.00
|
|
Samsung
|
40
|
1749.50
|
|
Sharp
|
32
|
1035.00
|
|
Samsung
|
52
|
2950.00
|
|
Sony
|
40
|
1908.50
|
|
Sony
|
52
|
3103.00
|
|
Sony
|
46
|
2606.00
|
|
Sony
|
46
|
2861.00
|
|
Sony
|
52
|
3434.00
|
a. Does there appear to be a linear relationship between the screen size and the price?
b. Which variable is the "dependent" variable?
c. Using statistical software, determine the regression equation. Interpret the value of the slope in the regression equation.
d. Include the manufacturer in a multiple linear regression analysis using a "dummy" variable. Does it appear that some manufacturers can command a premium price? Hint: You will need to use a set of indicator variables.
e. Test each of the individual coefficients to see if they are significant.
f. Make a plot of the residuals and comment on whether they appear to follow a nor¬mal distribution.
g. Plot the residuals versus the fitted values. Do they seem to have the same amount of variation?