A Certain Type of Rare Gem Serves as a Status $$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }$$

question 112

Essay

A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status the owners believe they gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model $$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }$$
where $y =$ Demand (in thousands) and $x =$ Retail price per carat (dollars).
This model was fit to data collected for a sample of 12 rare gems. A portion of the printout is given below:

$\begin{array}{lrrrrr}\text { SOURCE } & \text { DF } & 55 & \text { M5 } & \text { F } & \text { PR }>\text { F }\\\\\text { Model } & 2 & 115145 & 57573 & 373 & , 0001 \\\text { Error } & 9 & 1388 & 154 & & \\\text { TOTAL } & 11 & 116533 & &\end{array}$

$\text { Root MSE } \quad 12.42 \quad \text { R-Square } \quad 988$

$\begin{array}{lrrrr}\text { VARIABLES }& \text { ESTIMATES }& \text { STD, ERROR } &\text { PARAMETER =0 } & \text { P R>|T|}\\\\\text { INTERPCEP } & 286.42 & 9.66 & 29.64 & .0001 \\\mathrm{X} & -.31 & .06 & -5.14 & .0006 \\\mathrm{X} \cdot \mathrm{X} & .000067 & .00007 & .95 & .3647\end{array}$

Does the quadratic term contribute useful information for predicting the demand for the gem? Use $\alpha = .10$ .

Recognize the specific structures within the nasal cavity.

Differentiate between the anatomical characteristics of the right and left lungs.

Understand the roles of cartilages in the respiratory system.

Identify the location and function of the larynx, including related cartilages.

---

Definitions:

RFID

stands for Radio-Frequency Identification, a technology that uses electromagnetic fields to automatically identify and track tags attached to objects.

Fast Fashion

A term used to describe clothing collections which are based on the most recent fashion trends and are brought to market quickly at an affordable price.

SCM System

A Supply Chain Management System is an integrated software solution that manages and oversees the flow of goods, data, and finances as a product or service moves from supplier to customer.

Amazon

A multinational technology company primarily known for its e-commerce platform, cloud computing services, digital streaming, and artificial intelligence.