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

question 15

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

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

Interpret the coefficient of determination for the regression model.

• A) There is sufficient evidence to indicate that the size of the diamond is a useful predictor of the price of a diamond when testing at alpha \(= 0.05\).
• B) For every 1-carat increase in the size of a diamond, we estimate that the price of the diamond will increase by \(\$ 1117.56\).
• C) We can explain \(89.25 \%\) of the variation in the sampled diamond prices around their mean using the size of the diamond in a linear model.
• D) We expect most of the sampled diamond prices to fall within \(\$ 2235.12\) of their least squares predicted values.

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Definitions:

Premature

Occurring before the expected time or before the completion of the normal gestation period, often used to describe early birth.

Full-Term

Referring to a pregnancy that has reached between 39 and 40 weeks of gestation, indicating that the baby is fully developed and ready for birth.

Very Low Birth Weight

A term used to describe babies who are born weighing less than 1500 grams (3 pounds, 4 ounces).

Pounds

A unit of weight commonly used in the United States and the United Kingdom, equivalent to 0.453592 kilograms.