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

question 79

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

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

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

Interpret the standard deviation of the regression model.

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

---

Definitions:

Newborn Infants

Babies in the first weeks of life, typically considered to be from birth to one month of age.

Middle Aged

Pertaining to the period in human life that typically ranges from about 45 to 65 years of age.

Hepatitis A

A highly contagious viral infection of the liver caused by the hepatitis A virus, typically transmitted through ingestion of contaminated food or water.

Vehicle Borne-Transmission

The spread of disease through vehicles, such as cars or buses, which can act as a medium for transporting pathogens.