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

question 56

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 $\mathrm { R } ^ { 2 }$
-The table below shows the population of a city (in millions) in each year during the period 1990 - 1995. Using the number of years since 1990 as the independent variable, find the regression equation of the best model. $\begin{array}{l|llllll}\mathrm{x} & 1990 & 1991 & 1992 & 1993 & 1994 & 1995 \\\hline \mathrm{y} & 1.08 & 1.37 & 1.68 & 2.19 & 2.73 & 3.34\end{array}$

• A) \(y = 0.930 + 0.454 x\)
• B) \(y = 0.05 x ^ { 2 } + 0.27 x + 1.06\)
• C) \(y = 1.27 x ^ { 0.550 }\)
• D) \(y = 1.08 e ^ { 0.228 x }\)

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Definitions:

Central Limit Theorem

A theory stating that when samples are large enough, their mean will be approximately normally distributed, regardless of the population's distribution.

Standard Error

A statistical measure that quantifies the variability or dispersion of a sample statistic from the population parameter it estimates.

Population Distribution

A term that describes how the values of a variable are distributed across an entire population.

Sampling Distribution

The probability distribution of a given statistic based on a random sample.