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 determine the price of a single 1-carat diamond?
◦ 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.
◦ 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.
The relationship between free energy and electron movement along the electron transport chain
Gaser and Schlaug's study of the size of visual, motor, and auditory nuclei in the brains of mu
Relationship between psychosocial adaptation
Size of Particles
A close relationship between greenhouse gas emissions and a country’s gross domestic product
The price of rice in a small country is currently $6 per pound. In order to help low-income ...