What is the relationship between diamond price and carat size? 307 diamonds were
ID: 3224273 • Letter: W
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.