What Is the Relationship Between Diamond Price and Carat Size

question 85

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 $$\begin{array} { l c c c c c } \text { Predictor } & & & & \\\text { Variables } & \text { Coefficient } & \text { Std Error } & \text { T } & \text { P } & \\\text { Constant } & - 2298.36 & 158.531 & - 14.50 & 0.0000 & \\\text { Size } & 11598.9 & 230.111 & 50.41 & 0.0000 & \\& & & & & \\\text { R-Squared } & 0.8925 & \text { Resid. Mean Square (MSE) } & 1248950 \\\text { Adjusted R-Squared } & 0.8922 & { \text { Standard Deviation } } & 1117.56\end{array}$$ Interpret the coefficient of determination for the regression model.

• A) 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.
• B) 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.
• C) We expect most of the sampled diamond prices to fall within $2235.12 of their least squares predicted values.
• D) For every 1-carat increase in the size of a diamond, we estimate that the price of the diamond will increase by $1117.56.
• 11.6 Using the Model for Estimation and Prediction
• 1 Calculate and Compare Confidence Intervals for Mean of y

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Definitions:

Sample Size

The number of observations or subjects included in a study.

Effect Size

A quantitative measure of the magnitude of a phenomenon, used to indicate the size of an effect or difference found in a study.

Type I Error

The incorrect rejection of a true null hypothesis, or a "false positive," in hypothesis testing, indicating that the test suggests an effect that does not actually exist.

Type II Error

A statistical term referring to the error that occurs when a false null hypothesis is not rejected, indicating a false negative finding.