Reference no: EM131048356
World record running times. Exercise 28.15 (page 28-31) shows the progress of world record times (in seconds) for the 10,000-meter run for both men and women.
(a) Provide the ANOVA table for the regression model with two regression lines, one for men and one for women.
(b) Are all the individual coefficients significantly different from zero? Set up the appropriate hypotheses, identify the test statistics and P-values, and make conclusions in the context of the problem.
Example 28.15:
If there is a quadratic relationship between a quantitative variable y and another quantitative variable x1, the mean response is given by
A young couple are shopping for a diamond, so they are interested in learning more about how these gems are priced. They have heard about the 4 C's: carat, color, cut, and clarity. Is there is a relationship between these diamond characteristics and the price? Table 28.4 shows records for the first 10 diamonds in a large data base.6 The complete data base contains 351 diamonds and is available in the file DIAMONDS.dat. The variables include Carat, Color, Clarity, the Depth of the cut, the price per carat Price/Ct, and the Total Price. Since the young couple are primarily interested in the price of a diamond, they decide to begin by examining the relationship between Total Price and Carat. Figure 28.11 shows a scatterplot of Total Price versus Carat, along with the estimated quadratic
FIGURE 28.11:
regression model. Using the quadratic regression model, the couple estimate the mean price of a diamond to be
The couple are happy because they can explain 92.6% of the variation in the total price of the diamonds in the data base using this quadratic regression model. However, they are concerned because they used explanatory variables that are not independent. An explanatory variable and its square are obviously related to one another. The correlation between Carat (x1) and Carat2 (x12) is 0.952.
|
A multimedia statistics learning system
: A computer game. A multimedia statistics learning system includes a test of skill in using the computer's mouse. The software displays a circle at a random location on the computer screen.
|
|
The new multiple regression model
: Suppose that we also have data on a second treadmill, made by LifeFitness. An indicator variable for brand of treadmill, say Treadmill = 1 for Cybex and Treadmill= 0 for LifeFitness, is created for a new model.
|
|
How would you describe their role in the collaboration
: How would you clarify the rewards and benefits to these individuals? How would you describe their role in the collaboration? What questions they might ask you and how would you respond to their questions?
|
|
Predicting calories from these explanatory variables
: The equation for predicting calories from these explanatory variables is
|
|
Provide the anova table for the regression model
: World record running times. Exercise 28.15 (page 28-31) shows the progress of world record times (in seconds) for the 10,000-meter run for both men and women.
|
|
Some interaction terms and quadratic terms
: The clothing retailer problem. The scatterplot and histogram below show the residuals from the model in Example 28.20 with all explanatory variables, some interaction terms, and quadratic terms. Comment on both plots. Do you see any reason for con..
|
|
Implement an electronic record that can easily transferred
: Visualize three patient issues that may arise as a result of implementing an electronic record that can be easily transferred from clinic to physician.
|
|
Model for the clothing retailer problem
: Final model for the clothing retailer problem. The residual plots below show the residuals for the final model in the clothing retailer problem plotted against Purchase12 and Recency. Do the plots suggest any potential problems with the conditions..
|
|
Created to incorporate this relationship into the model
: Clothing retailer. Since the average purchase amount Purchase12 was such a good predictor, the manager would like you to consider another explanatory variable: the average purchase amount from the previous 12 months. Create the new variable
|