What Is the Relationship Between Diamond Price and Carat Size $= 0.05$

question 11

Multiple Choice

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


Interpret the coefficient of determination for the regression model.

• A) 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 \(= 0.05\).
• B) For every 1-carat increase in the size of a diamond, we estimate that the price of the diamond will increase by \(\$ 1117.56\).
• C) We expect most of the sampled diamond prices to fall within \(\$ 2235.12\) of their least squares predicted values.
• D) 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.

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