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

question 49

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 $\sum ( \mathrm { y } - \hat { \mathrm { y } } ) ^ { 2 }$ 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 power
model. Which model fits better? How can you tell? $\begin{array} { c | c c c c c } x & 1 & 2 & 3 & 4 & 5 \\\hline y & 3 & 9 & 17 & 30 & 40\end{array}$

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Definitions:

Qualitative

Pertaining to or concerning the quality of something rather than its quantity, often used in research to describe non-numerical data.

Quantitative

Refers to research methodologies that involve the collection and analysis of numerical data, used to identify patterns, relationships, or to test hypotheses.

Quantitative

Concerned with, evaluating, or determined by the amount of something rather than its quality.

Qualitative

Pertaining to research methods focused on collecting and analyzing non-numerical data (e.g., text, video) to understand concepts, thoughts, or experiences.