What Is the Relationship Between Diamond Price and Carat Size

question 29

Multiple Choice

What is the relationship between diamond price and carat size? 307 diamonds were sampled and a straight-line relationship was hypothesized between y = diamond price (in dollars) and x = size of the diamond (in carats) . The simple linear regression for the analysis is shown below: Least Squares Linear Regression of PRICE

$\begin{array}{lccccc}\text { Predictor}\\\text { Variables } & \text { Coefficient } & \text { Std Error } & \text { T } & \text { P } \\\text { Constant } & -2298.36 & 158.531 & -14.50 & 0.0000 \\\text { Size } & 11598.9 & 230.111 & 50.41 & 0.0000\end{array}$

$\begin{array}{lccc}\text { R-Squared } & 0.8925 & \text { Resid. Mean Square (MSE) } & 1248950 \\\text { Adjusted R-Squared } & 0.8922 & \text { Standard Deviation } & 1117.56\end{array}$

The model was then used to create 95% confidence and prediction intervals for y and for E(Y) when the carat size of the diamond was 1 carat. The results are shown here:
95% confidence interval for E(Y) : ($9091.60, $9509.40)
95% prediction interval for Y: ($7091.50, $11,510.00)
Which of the following interpretations is correct if you want to use the model to estimate E(Y) for all 1-carat diamonds?

• A) We are 95% confident that the average price of all 1-carat diamonds will fall between $7091.50 and $11,510.00.
• B) We are 95% confident that the price of a 1-carat diamond will fall between $7091.50 and $11,510.00.
• C) We are 95% confident that the price of a 1-carat diamond will fall between $9091.60 and $9509.40.
• D) We are 95% confident that the average price of all 1-carat diamonds will fall between $9091.60 and $9509.40.

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Definitions:

Sales Knowledge

Understanding and expertise about selling techniques, product details, and market dynamics.

Trade Advertising

A form of advertising aimed at businesses within a certain industry to promote products or services to them.

Industrial Advertising

Advertising targeted at individuals and organizations involved in manufacturing or business operations, rather than the general consumer.

Markup on Selling Price

The amount added to the cost price of goods to cover overhead and profit; the difference between the selling price and the product's cost.