For the Data Below, Determine the Logarithmic Equation $$\hat { y } = a + b \ln x$$

question 79

Multiple Choice

For the data below, determine the logarithmic equation, $$\hat { y } = a + b \ln x$$ that best fits the data. Hint: Begin by replacing each x-value with ln x then use the usual methods to find the equation of the least squares regression
Line. $\begin{array}{c|ccccl}\mathrm{x} & 1.2 & 2.7 & 4.4 & 6.6 & 9.5 \\\hline \mathrm{y} & 1.6 & 4.7 & 8.9 & 9.5 & 12.0\end{array}$

• A) \(\hat { y } = 0.457 + 5.06 \ln x\)
• B) \(\hat { y } = - 0.458 + 5.36 \ln x\)
• C) \(\hat { y } = - 1.81 + 6.91 \ln \mathrm { x }\)
• D) \(\hat { y } = 0.881 + 4.86 \ln \mathrm { x }\)

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Definitions:

Humans

The species Homo sapiens, characterized by bipedalism, high manual dexterity, and advanced cognitive abilities leading to the development of complex tools and society.

Cellulose

A complex carbohydrate that forms the primary structural component of plant cell walls.

Abnormally Folded

Refers to proteins that have not achieved their proper three-dimensional structure, often leading to diseases.

Prions

Misfolded proteins that can induce normal proteins to also misfold, leading to diseases in the nervous system.