SCENARIO 15-1
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices,
the demand increases and it 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 owners believe they gain in obtaining the gem. Thus, the model proposed to best explain
the demand for the gem by its price is the quadratic model: $Y = \beta _ { 0 } + \beta _ { 1 } X + \beta _ { 2 } X ^ { 2 } + \varepsilon$ where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the
computer analysis obtained from Microsoft Excel is shown below:
-Referring to Scenario 15-1, a more parsimonious simple linear model is likely to
be statistically superior to the fitted curvilinear for predicting sale price (Y).

Question

SCENARIO 15-1
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices,
the demand increases and it 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 owners believe they gain in obtaining the gem. Thus, the model proposed to best explain
the demand for the gem by its price is the quadratic model: $Y = \beta _ { 0 } + \beta _ { 1 } X + \beta _ { 2 } X ^ { 2 } + \varepsilon$ where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the
computer analysis obtained from Microsoft Excel is shown below: 
-Referring to Scenario 15-1, a more parsimonious simple linear model is likely to
be statistically superior to the fitted curvilinear for predicting sale price (Y).

Quizplus · Accepted Answer

A more parsimonious model is one that uses fewer parameters to explain the same amount of variance in the dependent variable. In this case, the simple linear model uses only two parameters (the intercept and the slope) to explain the variance in sale price, while the curvilinear model uses three parameters (the intercept, the slope, and the curvature). Therefore, the simple linear model is more parsimonious than the curvilinear model.

SCENARIO 15-1 a Certain Type of Rare Gem Serves as a Status

SCENARIO 15-1
a Certain Type of Rare Gem Serves as a Status