Construct a Scatterplot and Identify the Mathematical Model That Best $\mathrm { R } ^ { 2 }$

question 25

Multiple Choice

Construct a scatterplot and identify the mathematical model that best fits the data. Assume that the model is to be used
only for the scope of the given data and consider only linear, quadratic, logarithmic, exponential, and power models. Use
a calculator or computer to obtain the regression equation of the model that best fits the data. You may need to fit several
models and compare the values of $\mathrm { R } ^ { 2 }$
- $\begin{array}{c|cccccc}x & 1 & 2 & 3 & 4 & 5 & 6 \\\hline y & 9 & 13 & 25 & 27 & 31 & 46\end{array}$

• A) \(y = 3.14 + 6.59 x\)
• B) \(y = 1.07 + 6.89 x\)
• C) \(\mathrm { y } = 8.34 \mathrm { x } ^ { 0.88 }\)
• D) \(y = 4.87 + 18.5 \ln x\)

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Definitions:

Nominal Rates

Interest rates or rates of return that have not been adjusted for inflation, representing the face value of financial products.

Real Rates

Interest rates or rates of return that have been adjusted for inflation.

Gordon Growth Model

The Gordon Growth Model is a method to determine the intrinsic value of a stock based on a future series of dividends that grow at a constant rate.

Fisher Effect

An economic theory that describes the relationship between inflation and both real and nominal interest rates.