Which of the Following Is Not True About the Coefficient $r ^ { 2 }$

question 16

Multiple Choice

Which of the following is not true about the coefficient of determination, $r ^ { 2 }$ ?

• A) In order to interpret \(r ^ { 2 }\) the linearity condition of the linear regression model must be satisfied.
• B) The coefficient of determination, \(r ^ { 2 }\), is a statistic that will give some information about how well the data fits the model, but it should not be the only piece of information taken into consideration when determining how useful a linear model might be.
• C) A hypothesis test should be conducted verify that \(r ^ { 2 }\) is large enough to conclude a linear relationship exists.
• D) The coefficient of determination, \(r ^ { 2 }\), ranges from \(0 \%\) to \(100 \%\) and represents the amount of variability in the response variable \(( y )\) explained by the regression line.

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Definitions:

Synchronous Speed

The speed at which the magnetic field in an AC machine rotates, typically in motors or generators, determined by the machine's electrical frequency and the number of magnetic poles.

Rotor Speed

The rotational speed of the rotor in a motor or generator, typically measured in revolutions per minute (RPM).

Percent Slip

In an induction motor, the difference between the synchronous speed and the actual rotor speed, expressed as a percentage of the synchronous speed.

Three-Phase Motor

An electric motor that operates on three phases of alternating current, offering smoother and more efficient operation than single-phase motors for high-power applications.