What Is the Relationship Between Diamond Price and Carat Size $0.18$

question 36

Multiple Choice

What is the relationship between diamond price and carat size? 307 diamonds were sampled (ranging in size from $0.18$ to $1.1$ carats) 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

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

$\begin{array}{llll}\text { R-Squared } & 0.8925 & \text { Resid. Mean Square (MSE) } & 1248950\\\text { Adiusted R-Souared } & 08920 & \text { Standard Deviation } & 111756\end{array}$
Interpret the estimated y-intercept of the regression line.

• A) No practical interpretation of the y-intercept exists since a diamond of 0 carats cannot exist and falls outside the range of the carat sizes sampled.
• B) When a diamond is 11598.9 carats in size, we estimate the price of the diamond to be $2298.36.
• C) When a diamond is 0 carats in size, we estimate the price of the diamond to be $2298.36.
• D) When a diamond is 0 carats in size, we estimate the price of the diamond to be $11,598.90.

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