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

question 109

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

$\begin{array}{l}\text { Predictor }\\\begin{array}{lcccll}\text { Variables } & \text { Coefficient } & \text { Std Error } & \text { T } & {\text { P }} \\\text { Constant } & -2298.36 & 158.531 & -14.50 & 0.0000 \\\text { Size } & 11598.9 & 230.111 & 50.41 & 0.0000\end{array}\end{array}$

$\begin{array}{lccc}\text { R-Squared } & 0.8925 & \text { Resid. Mean Square (MSE) } & 1248950 \\\text { Adjusted R-Squared } & 0.8922 & \text { Standard Deviation } & 1117.56\end{array}$


Which of the following assumptions is not stated correctly?

• A) The values of \(\varepsilon\) associated with any two observations are dependent on one another.
• B) The mean of the probability distribution of \(\varepsilon\) is 0 .
• C) The probability distribution of \(\varepsilon\) is normal.
• D) The variance of the probability distribution of \(\varepsilon\) is constant for all settings of the independent variable.

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