Provide an Appropriate Response $\begin{array} { r r r r r r } x & 1.2 & 2.7 & 4.4 & 6.6 & 9.5 \\\hline y & 1.6 & 4.7 & 8.9 & 9.5 & 12.0\end{array}$

question 53

Multiple Choice

Provide an appropriate response. 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.
$\begin{array} { r r r r r r } x & 1.2 & 2.7 & 4.4 & 6.6 & 9.5 \\\hline y & 1.6 & 4.7 & 8.9 & 9.5 & 12.0\end{array}$

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

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Definitions:

StdDev

A measurement that quantifies the amount of variation or dispersion in a set of data values, same as Standard Deviation.

Mean

The mean value of a collection of numbers, obtained by dividing the total sum of the numbers by the quantity of numbers in the collection.

Median

The middle value in a dataset when it is arranged in ascending or descending order, or the average of the two middle values when the dataset has an even number of observations.

Interquartile Range

A measure of variability, calculated as the difference between the 25th and 75th percentiles of a data set.