What Is the Relationship Between Diamond Price and Carat Size $0.18$

question 36

Multiple Choice

What is the relationship between diamond price and carat size? 307 diamonds were sampled (ranging in size from $0.18$ to $1.1$ carats) 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

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

$\begin{array}{llll}\text { R-Squared } & 0.8925 & \text { Resid. Mean Square (MSE) } & 1248950\\\text { Adiusted R-Souared } & 08920 & \text { Standard Deviation } & 111756\end{array}$
Interpret the estimated y-intercept of the regression line.

• A) No practical interpretation of the y-intercept exists since a diamond of 0 carats cannot exist and falls outside the range of the carat sizes sampled.
• B) When a diamond is 11598.9 carats in size, we estimate the price of the diamond to be $2298.36.
• C) When a diamond is 0 carats in size, we estimate the price of the diamond to be $2298.36.
• D) When a diamond is 0 carats in size, we estimate the price of the diamond to be $11,598.90.

---

Definitions:

Progressive Reformers

Individuals or groups advocating for social, political, and economic reform in the late 19th and early 20th centuries to address problems stemming from industrialization, urbanization, and corruption.

Social Legislation

Laws enacted to address social issues and protect the welfare of citizens, including healthcare, education, and housing.

Margaret Sanger

Margaret Sanger was an American birth control activist, sex educator, and nurse who played a pivotal role in the legalization and development of contraception and family planning services in the United States.

Activism

The policy or action of using vigorous campaigning to bring about political or social change.