What Is the Relationship Between Diamond Price and Carat Size

question 24

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 $$\begin{array}{l}\text { Predictor }\\\begin{array} { l c c c l l } \text { Variables } & \text { Coefficient } & \text { Std Error } & \text { T } & \text { P } \\\text { Constant } & - 2298.36 & 158.531 & - 14.50 & 0.0000 \\\text { Size } & 11598.9 & 230.111 & 50.41 & 0.0000\end{array}\\\\\begin{array} { l c c c } \text { R-Squared } & 0.8925 & \text { Resid. Mean Square (MSE) } & 1248950 \\\text { Adjusted R-Squared } & 0.8922 & \text { Standard Deviation } & 1117.56\end{array}\end{array}$$ The model was then used to create 95% confidence and prediction intervals for y and for E(Y) when the carat size of the diamond was 1 carat. The results are shown here: 95% confidence interval for E(Y) : ($9091.60, $9509.40) 95% prediction interval for Y: ($7091.50, $11,510.00) Which of the following interpretations is correct if you want to use the model to estimate E(Y) for all 1-carat diamonds?

• A) We are 95% confident that the price of a 1-carat diamond will fall between $7091.50 and $11,510.00.
• B) We are 95% confident that the average price of all 1-carat diamonds will fall between $7091.50 and $11,510.00.
• C) We are 95% confident that the price of a 1-carat diamond will fall between $9091.60 and $9509.40.
• D) We are 95% confident that the average price of all 1-carat diamonds will fall between $9091.60 and $9509.40.