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) \(\hat { y } = 0.881 + 4.86 \ln \mathrm { x }\)

---

Definitions:

Press Button

A simple mechanism that, when pressed, activates or controls a device.

Payoff

The outcome of a decision or action, usually quantified in terms of profit or utility.

Nash Equilibrium

A concept in game theory where no player can benefit by changing their strategy while the other players keep theirs unchanged.

Michigan Football

The football program representing the University of Michigan in college football competitions.