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) $\hat { y } = - 1.81 + 6.91 \ln x$

Question

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}

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

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) $\hat { y } = - 1.81 + 6.91 \ln x$

Quizplus · Accepted Answer

After replacing each $x$-value with $\ln x$, the least squares regression line is calculated, resulting in the equation $\hat { y } = 0.457 + 5.06 \ln x$.

For the Data Below, Determine the Logarithmic Equation y=a+bln⁡xy = a + b \ln xy=a+blnx

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