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
Variables Coefficient Std Error T P
Constant -2298.36 158.531 -14.50 0.0000
Size 11598.9 230.111 50.41 0.0000
R-Squared 0.8925 Resid. Mean Square (MSE) 1248950
Adjusted R-Squared 0.8922 Standard Deviation 1117.56
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?
◦ We are 95% confident that the average price of all 1-carat diamonds will fall between $7091.50 and $11,510.00.
◦ We are 95% confident that the price of a 1-carat diamond will fall between $9091.60 and $9509.40.
◦ We are 95% confident that the price of a 1-carat diamond will fall between $7091.50 and $11,510.00.
◦ We are 95% confident that the average price of all 1-carat diamonds will fall between $9091.60 and $9509.40.
Use of fluorescent molecules by Lowenstein and colleagues to determine the size of gap-junction chan
Beak size and Drought
The relationship between the permissible exposure limit (PEL), the short-term exposure limit (STEL), ...
Relationship between Latitude and Income per Capita
Distribution Patterns and Population Size Estimates (Bio 30)
Changes in the size of the thoracic cavity during the respiratory cycle