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:

Cocoon

A protective casing spun by the larvae of many insects (like moths and butterflies) and some other animals, where they undergo metamorphosis into their adult forms.

Clams

Aquatic bivalve mollusks known for their soft bodies enclosed within a hinged shell, often consumed as seafood or used in research.

Filter-Feeders

Organisms that feed by straining suspended matter and food particles from water, commonly found in aquatic environments.

Toxins

Poisonous substances produced by living organisms, often causing disease when entered into the body at sufficient quantities.