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

question 79

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

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

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

Interpret the standard deviation of the regression model.

• A) We expect most of the sampled diamond prices to fall within $2235.12 of their least squares predicted values.
• B) 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.
• C) For every 1-carat increase in the size of a diamond, we estimate that the price of the diamond will increase by $1117.56.
• D) We expect most of the sampled diamond prices to fall within $1117.56 of their least squares predicted values.