Construct a Scatterplot and Identify the Mathematical Model That Best

question 9

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 R²
-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) \(y = 1.27 x ^ { 0.550 }\)
• B) \(y = 0.05 x ^ { 2 } + 0.27 x + 1.06\)
• C) \(y = 1.08 e ^ { 0.228 x }\)
• D) \(y = 0.930 + 0.454 x\)

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Definitions:

Management Discussion And Analysis

A section in an annual report where management provides insight and perspective on the financial results, trends, and future outlook of the company.

Return On Stockholders' Equity

A financial ratio that measures a company's ability to generate profits from its shareholders' equity.

Return On Common Stockholders' Equity

A measure of financial performance that indicates how much net income a company generates with the money shareholders have invested.

Earnings Per Share

A financial measure that calculates the portion of a company’s profit allocated to each outstanding share of common stock, indicating profitability.