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:

Turner's Syndrome

A chromosomal disorder affecting females, characterized by the absence of all or part of a second sex chromosome.

Infertile

The inability to conceive children or young after a period of time, usually a year or more of regular sexual activity without contraception.

Down Syndrome

A genetic disorder caused by the presence of all or part of a third copy of chromosome 21, characterized by physical growth delays, characteristic facial features, and often intellectual disability.

Extra Chromosome

The presence of an additional chromosome in an individual's genetic makeup, which can result in developmental disorders such as Down syndrome.