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

question 90

Essay

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 sum of squares of residuals $\sum ( y - \hat { y } ) ^ { 2 }$ can be used to assess the quality of a regression model. A residual is
the difference between an observed y value and the value of y predicted from the model, $\hat { y }$ . The better the
model, the smaller the sum of squares of residuals. For the data below find the sum of squares of residuals
which results from fitting a linear model, and the sum of squares of residuals which results from fitting a
logarithmic model. Which model fits better? How can you tell? $\begin{array} { c | c c c c c } x & 1 & 2 & 3 & 4 & 5 \\\hline y & 7 & 17 & 20 & 25 & 28\end{array}$

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Definitions:

Horizontal Merger

Merger that joins firms in the same industry for the purpose of diversification, increasing customer bases, cutting costs, or expanding product lines.

Vertical Merger

Merger that combines firms operating at different levels in the production and marketing process.

Joint Venture

A business arrangement in which two or more parties agree to pool their resources for the purpose of accomplishing a specific task, project, or other business activity.

Conglomerate Company

A Conglomerate Company is a large corporation composed of several companies with diverse or unrelated business interests.