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

question 129

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 $\mathrm { R } ^ { 2 }$
- $\begin{array}{c|ccccc}\mathrm{x} & 1 & 2 & 3 & 4 & 5 \\\hline \mathrm{y} & 7 & 17 & 20 & 25 & 28\end{array}$

• A) \(y = 6.81 \mathrm { e } ^ { 0.316 \mathrm { x } }\)
• B) \(y = 7.19 + 12.8 \ln x\)
• C) \(\mathrm { y } = 4.40 + 5.00 \mathrm { x }\)
• D) \(\mathrm { y } = 7.82 \mathrm { x } ^ { 0.844 }\)

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Definitions:

Equilibria

The condition in which all competing influences are balanced in a wide variety of contexts, including economics where supply equals demand.

Markets

Systems, institutions, or environments where buyers and sellers interact to exchange goods, services, or information.

Technological Change

Adjustments or improvements in the method of production, invention, and innovation in processes that often lead to increased productivity.

Microwave Ovens

Appliances that use microwave radiation to cook or heat food, offering a quick and convenient method of food preparation.