What is the relationship between diamond price and carat size? 307 diamonds were

Question

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.

Explanation / Answer

Clearly from the above table we get the following relationship between the diamond price and the carat size:

Diamond price = Constant + Size_Coefficient* Carat Size

Putting the values of coefficients from the above table we get:

Diamond price = -2298.36 + 11598.9*Carat Size

This is the required regression equation.

Interpretation of slope: A slope value of 11598.9 indicates that for every unit increase in the carat size, there is 11598.9 units increase in the diwmond price.

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