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
Interpret the estimated slope of the regression line.
◦ For every 2298.36-carat decrease in the size of a diamond, we estimate that the price of the diamond will increase by $11,598.90.
◦ For every 1-carat increase in the size of a diamond, we estimate that the price of the diamond will decrease by $2298.36.
◦ For every 1-carat increase in the size of a diamond, we estimate that the price of the diamond will increase by $11,598.90.
◦ For every $1 decrease in the price of the diamond, we estimate that the size of the diamond will increase by 11,598.9 carats.
The mark-recapture technique is often used to estimate population size.
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