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

question 18

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

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

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

Which of the following conclusions is correct when testing to determine if the size of the diamond is a useful positive linear predictor of the price of a diamond?

• A) There is sufficient evidence to indicate that the size of the diamond is a useful positive linear predictor of the price of a diamond when testing at \(\alpha = 0.05\).
• B) The sample size is too small to make any conclusions regarding the regression line.
• C) There is insufficient evidence to indicate that the price of the diamond is a useful positive linear predictor of the size of a diamond when testing at \(\alpha = 0.05\).
• D) There is insufficient evidence to indicate that the size of the diamond is a useful positive linear predictor of the price of a diamond when testing at \(\alpha = 0.05\).

Explain the concepts of psychological and physical dependence on psychoactive drugs.

Distinguish among depressants, stimulants, and hallucinogens and their effects on physical and psychological functioning.

Understand the reasons for sleep and its importance to psychological and physical health.

Describe the difference between automatic and controlled processes.

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Definitions:

Perfectly Competitive Industry

An industry characterized by many buyers and sellers, where no single entity can influence the market price of the product.

Marginal Cost

The price of manufacturing an incremental unit of a product.

Perfectly Competitive Market

A market structure characterized by an infinite number of buyers and sellers, identical products, no barriers to entry or exit, and perfect information among all participants.

Short-run Industry

A period in which at least one factor of production is fixed, and firms can only partially adjust their production levels.