What Is the Relationship Between Diamond Price and Carat Size $y =$

question 33

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

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

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

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 determine the price of a single 1-carat diamond?

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

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Definitions:

Margin

The difference between the selling price of a product and the cost of the product, representing profitability.

Sales

The total revenue earned from the sale of goods or services related to a company's primary operations.

Manufacturing Cycle Efficiency

A measure of the efficiency of the production process, calculated as value-added time divided by the total cycle time.

Value-added Time

The period during which a product or service is being modified or enhanced to increase its value to the customer.