Step 1

We construct a scatterplot in minitab. After entering the data, go to \(\displaystyle\text{Graphs}\rightarrow\text{Scatterplot}\)

Step 2

We can observe from scatterplot that any of power or quadratic model will fit best.

Using minitab, go to \(\displaystyle\text{Stats}\rightarrow\text{Regression}\rightarrow\text{Fit Regression Model}\)

Select scale value in responses and sound intensity in predictors.

The regression equation and \(\displaystyle{R}^{{{2}}}\) values for the models are given below. Since \(\displaystyle{R}^{{{2}}}={1}\) for logarithmic model.

Hence we conclude that logarithmic model is best fit. And the regression equation is:

\(\displaystyle{y}={0.0048}+{\left({4.34263}\right)}{\ln{{x}}}\)

\[\begin{array}{|c|c|}\hline \text{Model} & R^{2} & \text{Regression Equation} \\ \hline \text{Linear} & 0.8599 & y=26.14+(0.002343)x \\ \hline \text{Logarithmic} & 1 & 0.0048+(4.34263)\ln x \\ \hline \text{Power} & 0/9963 & (11.1995)x^{0.141221} \\ \hline \text{Quadratic} & 0/9751 & 23.837+(0.00614)x+(0.000001)x^{2} \\ \hline \text{Exponential} & 0.8147 & (26.26)1.0007^{x} \\ \hline \end{array}\]

We construct a scatterplot in minitab. After entering the data, go to \(\displaystyle\text{Graphs}\rightarrow\text{Scatterplot}\)

Step 2

We can observe from scatterplot that any of power or quadratic model will fit best.

Using minitab, go to \(\displaystyle\text{Stats}\rightarrow\text{Regression}\rightarrow\text{Fit Regression Model}\)

Select scale value in responses and sound intensity in predictors.

The regression equation and \(\displaystyle{R}^{{{2}}}\) values for the models are given below. Since \(\displaystyle{R}^{{{2}}}={1}\) for logarithmic model.

Hence we conclude that logarithmic model is best fit. And the regression equation is:

\(\displaystyle{y}={0.0048}+{\left({4.34263}\right)}{\ln{{x}}}\)

\[\begin{array}{|c|c|}\hline \text{Model} & R^{2} & \text{Regression Equation} \\ \hline \text{Linear} & 0.8599 & y=26.14+(0.002343)x \\ \hline \text{Logarithmic} & 1 & 0.0048+(4.34263)\ln x \\ \hline \text{Power} & 0/9963 & (11.1995)x^{0.141221} \\ \hline \text{Quadratic} & 0/9751 & 23.837+(0.00614)x+(0.000001)x^{2} \\ \hline \text{Exponential} & 0.8147 & (26.26)1.0007^{x} \\ \hline \end{array}\]