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

Predictor

VariablesCoefficientStd ErrorTP

Constant-2298.36158.531-14.500.0000

Size11598.9230.11150.410.0000

R-Squared0.8925Resid. Mean Square (MSE)1248950

Adjusted R-Squared0.8922Standard Deviation1117.56

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?