What is the relationship between diamond price and carat size? 307 diamonds were sampled (ranging in size from 0.18 to 1.1 carats) 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
Interpret the estimated y-intercept of the regression line.
◦ When a diamond is 0 carats in size, we estimate the price of the diamond to be $2298.36.
◦ When a diamond is 0 carats in size, we estimate the price of the diamond to be $11,598.90.
◦ When a diamond is 11598.9 carats in size, we estimate the price of the diamond to be $2298.36.
◦ No practical interpretation of the y-intercept exists since a diamond of 0 carats cannot exist and falls outside the range of the carat sizes sampled.
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