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

question 18

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

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

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

Which of the following conclusions is correct when testing to determine if the size of the diamond is a useful positive linear predictor of the price of a diamond?

• A) There is sufficient evidence to indicate that the size of the diamond is a useful positive linear predictor of the price of a diamond when testing at \(\alpha = 0.05\).
• B) The sample size is too small to make any conclusions regarding the regression line.
• C) There is insufficient evidence to indicate that the price of the diamond is a useful positive linear predictor of the size of a diamond when testing at \(\alpha = 0.05\).
• D) There is insufficient evidence to indicate that the size of the diamond is a useful positive linear predictor of the price of a diamond when testing at \(\alpha = 0.05\).

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Definitions:

Supply Curve

A visual depiction that showcases the connection between the cost of a product and the amount available for sale.

Demand Curve

A graph showing the quantity of a good that consumers are willing and able to purchase at various prices.

Imposed Price

A price that is set by an external authority rather than by market forces of supply and demand.

Consumer-friendly

Describes goods, services, or policies that are designed with the welfare or satisfaction of consumers in mind.