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

question 15

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

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

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 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.
• D) We expect most of the sampled diamond prices to fall within \(\$ 2235.12\) of their least squares predicted values.

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Definitions:

Expectations-States Theory

Expectations-States Theory proposes that social hierarchies and expectations about individuals' performances in a group are formed based on societal stereotypes and perceptions, influencing group dynamics and member roles.

Work Group

A group of employees working towards common goals and objectives, often within the same department or unit of an organization.

French And Raven's

This elaborates on the original French and Raven model by presenting a framework for understanding social influence in groups through the dynamics of power.

Power Bases

refer to the sources of power or authority an individual or group holds, such as expertise, coercion, or referent power.