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:

Market Segmentation

The process of dividing a target market into smaller, more defined categories of consumers who share similar characteristics and needs.

Demographic Segmentation

The process of dividing a market into segments based on variables such as age, gender, income, education, or ethnicity.

Personal Factors

Individual characteristics such as age, income, education, and personal values that influence a person's behavior and decisions.

Consumer Behavior

The study of how individual customers, groups, or organizations select, buy, use, and dispose goods, services, ideas, or experiences to satisfy their needs and desires.