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:

Force Field Model

A framework proposed by Kurt Lewin to analyze the factors (forces) that influence the change process, with forces aiding change termed as driving forces and those opposing as restraining forces.

Restraining Forces

Factors that hinder or limit the process of change within an organization or individual's behavior.

Changed Behaviors

Modifications or adjustments in one's actions or reactions as a result of experiences or interventions.

Lewin's Change Model

A theoretical model for understanding organizational or personal change, involving three stages: unfreezing, changing, and refreezing.