Question

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 face the data you may need to fit several models and compare the values of R2

Answer 1

From the table, we construct the scatter plot:

As we can see, the plot shows an exponential or power behavior, so we use these models. Finding the best parameters of the fit leads to the equations:

`\begin{gathered} y=11.46e^(0.102x)\text{ \lparen Exponential model\rparen} \\ \\ y=0.45x^(1.903)\text{ \lparen Power-law model\rparen} \end{gathered}`

To decide which model best describes the data, we compare the values or R²:

`\begin{gathered} R^2=0.9604\text{ \lparen Exponential model\rparen} \\ \\ R^2=0.9993\text{ \lparen Power-law model\rparen} \end{gathered}`

And the fits are:

Answer: Last option (Power-law model)