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.

CD Yields The table lists the value y (in dollars) of $1000 deposited in a certificate of deposit at Bank of New York (based on rates currently in effect).

Table showing years and corresponding CD values in dollars for $1000 deposits at Bank of New York.

Accepted Answer

Hello. In this video, we are given that the following data lists the number of electric vehicles sold over several years. We want to construct a scatter plot to determine the best fitting mathematical model for the data set. Now in order to do or to create a scatter plot, we are going to need to use an external tool. In this video, I'm going to be using Google Sheets, but what we want to go ahead and do is we want to go ahead and take the given data set 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 went ahead and I created two separate columns. The first column represents the years for which the cars are being sold in, and the second column represents all the sales that are made within their respective years. Now, in order to create the scatter plot, the first thing we want to do is we want to go ahead and select both of the columns. Then we are going to go up to insert, and we are going to click on chart. Now this is going to create a chart for the sales versus the years, but we want to go ahead and make this a scatter plot. In order to change this to a scatter plot, we will go underneath chart type and we will select scatter. So now what we have is the scatter plot, and we can use the scatter plot to determine the best fitting model for the data set. Now, in order to determine the best fitting model, we are going to use the trend line tool. In order to activate a trend line tool, we will first click on one of the data points, and we are going to scroll down until we see a trend line option. We will select that. Now what this is going to do is it's going to create a trend line for different models for the sales or for the data points, and we are going to be looking at 4 different options. We have linear, exponential, logarithmic, and polynomial. And one thing to note here is that polynomial is another way of saying quadratic. So let's go ahead and start by taking a look at the linear model. Now, if we take a look at the linear model, many of the data points are either slightly above or slightly below, but never directly on the model, so this model doesn't fit the data set that well. Looking at exponential, exponential doesn't cover the entirety of the model, so this won't be an option either. If we take a look at logarithmic, it has a very similar shape to linear, which means that many of the data points are slightly above or below the trend line. So logarithmic wouldn't be a good pick either. Now when we pick polynomial, we want to make sure that our degree is 2. That way we are working with an accurate coefficient of determination. But if we are taking a look at the polynomial model, notice that many of the data points lie on the, on the trend line itself. So what this tells us is that the accurate model to pick for the scattered plot is going to be polynomial. And so with that being said, The correct solution to this problem is going to be option D. Quadratic is going to be the best fitting model for the sales over the years. 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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