Construct a scatterplot and identify the mathematical model that best fits the g

actever6a

actever6a

Answered question

2021-11-17

Construct a scatterplot and identify the mathematical model that best fits the given 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.
The table li sts intensities of sounds as multiples of a basic reference sound. A scale similar to the decibel scale is used to measure the sound intensity.
Sound Intensity31650075020005000Scale Value25.027.028.7533.037.0

Answer & Explanation

Ancessitere

Ancessitere

Beginner2021-11-18Added 17 answers

Step 1
We construct a scatterplot in minitab. After entering the data, go to GraphsScatterplot

Step 2
We can observe from scatterplot that any of power or quadratic model will fit best.
Using minitab, go to StatsRegressionFit Regression Model
Select scale value in responses and sound intensity in predictors.
The regression equation and R2 values for the models are given below. Since R2=1 for logarithmic model.
Hence we conclude that logarithmic model is best fit. And the regression equation is:
y=0.0048+(4.34263)lnx
ModelR2Regression EquationLinear0.8599y=26.14+(0.002343)xLogarithmic10.0048+(4.34263)lnxPower0/9963(11.1995)x0.141221Quadratic0/975123.837+(0.00614)x+(0.000001)x2Exponential0.8147(26.26)1.0007x

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