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

question 99

Multiple Choice

For the data below, determine the logarithmic equation, $y = a + b \ln x$ 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 1
$\begin{array}{c|ccccc}\mathrm{x} & 1.2 & 2.7 & 4.4 & 6.6 & 9.5 \\\hline \mathrm{y} & 1.6 & 4.7 & 8.9 & 9.5 & 12.0\end{array}$

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

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Definitions:

Propanoyl Chloride

An acyl chloride derived from propanoic acid, used in organic synthesis to introduce the propanoyl functional group.

Organic Product

A compound or material derived from living organisms, structured primarily around carbon chains or rings.

Methyl Thioacetate

An organosulfur compound used as a chemical intermediate, characterized by a sulfur atom bonded to an acetyl and a methyl group.

One Carbon Compounds

Organic compounds that contain only one carbon atom, often involved in fundamental biochemical processes.