The Following Statement About the Sample Correlation Coefficient Is True ${ r} ^ { 2 } _{ X Y }$

question 15

Multiple Choice

The following statement about the sample correlation coefficient is true.

• A)-1 ? r_X,Y ? 1.
• B) \({ r} ^ { 2 } _{ X Y }\) \(\stackrel { p } { \rightarrow }\) corr(X_i, Y_i).
• C)| r_X,Y | < 1.
• D)r_X,Y = \(\frac { S _ { x y } ^ { 2 } } { S _ { x } ^ { 2 } S _ { y } ^ { 2 } }\)

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Definitions:

Technological Improvements

Enhancements or advancements in technology that increase production efficiency, product quality, or introduce new goods and services.

Full Employment

A situation in which all available labor resources are being used in the most economically efficient way, typically characterized by the absence of cyclic unemployment.

Production Efficiency

A level of production in which the economy can no longer produce additional amounts of a good without lowering the production level of another product.

Production Inefficiency

A situation where a firm or economy is not producing at the lowest possible cost or maximally utilizing its resources, leading to waste or lost potential output.