Construct a Scatterplot and Identify the Mathematical Model That Best $\mathrm { R } ^ { 2 }$

question 107

Multiple Choice

Construct a scatterplot and identify the mathematical model that best fits the data. Assume that the model is to be used
only for the scope of the given data and consider only linear, quadratic, logarithmic, exponential, and power models. Use
a calculator or computer to obtain the regression equation of the model that best fits the data. You may need to fit several
models and compare the values of $\mathrm { R } ^ { 2 }$
-A rock is dropped from a tall building and its distance (in feet) below the point of release is recorded as accurately as possible at various times after the moment of release. The results are shown in the table. Find the
Regression equation of the best model. $\begin{array}{l|llllll}\mathrm{x} \text { (seconds after release) } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \mathrm{y} \text { (distance in feet) } & 16 & 63 & 146 & 255 & 403 & 572\end{array}$

• A) \(y = 13.0 \mathrm { e } ^ { 0.686 \mathrm { x } }\)
• B) \(y = - 74.9 + 290 \ln x\)
• C) \(y = - 148.4 + 112 x\)
• D) \(\mathrm { y } = 15.95 \mathrm { x } ^ { 2 }\)

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Definitions:

Organizational Behaviour Modification

A technique used within organizational psychology to improve employee behavior through a system of rewards and penalties.

Self-regulation

The ability of an individual to manage their own thoughts, emotions, and behaviors to achieve goals or adhere to standards.

Triadic Reciprocal Causation

A model in psychology that explains human behavior with the interaction between personal factors, behavior, and environmental factors.

Behaviour Modelling Training

A training method that involves observing, learning, and then replicating the behavior of a role model.