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 coefficient of determination for the regression model.
◦ We expect most of the sampled diamond prices to fall within $2235.12 of their least squares predicted values.
◦ We can explain 89.25% of the variation in the sampled diamond prices around their mean using the size of the diamond in a linear model.
◦ For every 1-carat increase in the size of a diamond, we estimate that the price of the diamond will increase by $1117.56.
◦ There is sufficient evidence to indicate that the size of the diamond is a useful predictor of the price of a diamond when testing at alpha = 0.05.
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