Finding the Best Model
In Exercises 5–16, construct a sc...

Question

Finding the Best Model

In Exercises 5–16, 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.

Richter Scale The table lists different amounts (metric tons) of the explosive TNT and the corresponding value measured on the Richter scale resulting from explosions of the TNT.

Table showing TNT amounts in metric tons and corresponding Richter scale values from explosions.

Accepted Answer

Hello. In this video, we are told that a small manufacturing company recorded its quarterly profits over the 1st 2 years of operation, and the data is given in the following chart. We want to analyze this data to identify the best fitting mathematical model. We want to create a scattered plot of profit versus quarter number, then apply a regression fit that fits each model and compare the goodness of fit using the coefficient determination. OK, so in order to start this problem, we need to go ahead and create a scatter plot. Now, in order to create the scatter plot, we are going to be using an external tool, which in this case, I'm going to be using Google Sheets. So what we're going to do is we're going to take the given the given data and separate it into two columns in Google Sheets. So let's go ahead and do that. So what I've done here is I've created two columns in Google Sheets. The first column represents the quarter and the second column represents the profits. Now in order to create the scatter plot, the first thing we're going to do is we're going to select both of the columns. Then we're going to go up to insert, and we are going to insert a chart for the data set. Now in this case here, this is not a scatter plot, but what we can do is we can go underneath chart type and select the scatter chart option, and now we have a scatter plot. So now in order to determine which model best fits the data, we are going to use the tool called the trend line. In order to enable the trend line, we will click on one of the data points, and we will scroll down until we find the trend line option. To enable it, we will click it, and we can now scroll through the different models. That we have that we have available to us. So we're going to be comparing the four models which is linear, exponential, logarithmic, and polynomial, and polynomial is another way of saying quadratic. So starting with the linear model, the linear model doesn't fit the data set that well since many of the points are either above or below the data, the trend line, so this won't be an option. Looking at exponential, exponential fits a little bit better, but there are still the issue of having some data points above or below the trend line. Logarithmic doesn't follow the pattern of the of the scattered plot at all, so this won't be an option. Now, when we're working with polynomial, we want to make sure that the polynomial is degree 2, so that we have an accurate coefficient of representation coefficient of determination. And if we're taking a look, this model better fits the data set than compared to the exponential model. So this is going to be the solution to the problem. The best fitting model is going to be the quadratic model, and therefore the correct option to the problem is going to be option B. So I hope this video helps you in understanding on how to approach this problem, and we will go ahead and see you all in the next video.

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