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

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.