Reference no: EM131048414
Diamonds. Specify the population regression model for predicting the total price of a diamond from two interacting variables, Carat and Depth (see Example 28.15 on page 28-35).
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.
|
Financially pressed by restrictions on reimbursement
: Pareto charts. Pareto charts are bar graphs with the bars ordered by height. They are often used to isolate the "vital few" categories on which we should focus our attention. Here is an example
|
|
Information on a key step within the process
: Process measurement. Based on your description of the process in Exercise 27.1, suggest specific variables that you might measure in order to
|
|
Actual business or manufacturing processes
: Describe a process. Choose a process that you know well. If you lack experience with actual business or manufacturing processes, choose a personal process such as ordering something over the Internet, paying a bill online, or recording a TV show o..
|
|
Conducted using a geiger-mueller tube in a physics lab
: Radioactive decay. An experiment was conducted using a Geiger-Mueller tube in a physics lab. Geiger-Mueller tubes respond to gamma rays and to beta particles (electrons). A pulse that corresponds to each detection of a decay product is produced, a..
|
|
Quadratic relationship between a quantitative variable
: Diamonds. Specify the population regression model for predicting the total price of a diamond from two interacting variables, Carat and Depth (see Example 28.15 on page 28-35).
|
|
Complete the financial concepts worksheet
: Complete the Financial Concepts Worksheet in 700 to 1,050 words. Explain each financial concept in your own words.
|
|
Researchers showed that the square root of the number
: Nest humidity and fleas. In the setting of Exercise 28.7 (page 28-16), researchers showed that the square root of the number of adult fleas y has a quadratic relationship with the nest humidity index x. Specify the population regression model for ..
|
|
Analysis of conflict by applying theory to a situation
: Define the context of the conflict, providing relevant history and limitations of study - examine major issues of conflict and their causes in that context - analysis of conflict by applying theory to a particular situation
|
|
What argument from rechels is made through the story of jack
: Explain two ways according to Gay-Williams that euthanasia Goes against ones best interests. Are you convinced? What argument from Rechels is made through the story of jack? Does Rechels have a valid point here?
|