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:

Natural-Kinds

Categories of objects and entities in the world that are thought to reflect a natural order, often discussed in philosophy and cognitive science.

Social-Kinds

Categories into which social entities are divided into based on shared Characteristics or attributes, often used in discussions of social taxonomy and identity.

Similarity-Based Approach

A method or strategy used in various fields, including psychology and computer science, that emphasizes analyzing and organizing items based on their similarities.

Knowledge-Based

Relating to systems or approaches that utilize a large repository of knowledge to solve problems or make decisions.