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

question 28

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 line.

$\begin{array}{c|ccccc}\mathrm{x} & 1.2 & 2.7 & 4.4 & 6.6 & 9.5 \\\hline \mathrm{y} & 1.6 & 4.7 & 8.9 & 9.5 & 12.0\end{array}$

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

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Definitions:

Probability Density Functions

Functions that describe the relative likelihood for a continuous random variable to take on a given value.

Continuous Random Variables

Variables that can take an infinite number of values within a given range, often associated with measurements in time, distance, or temperature.

Area Under the Curve

A measure used in various statistical analyses to quantitatively summarize the shape of a curve, often related to the performance of a model or the distribution of data.

Standard Normal Random Variable

A random variable that has a mean of zero and a standard deviation of one, following a normal distribution.