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.

Detecting Fraud Leading digits of check amounts are often analyzed for the purpose of detecting fraud. The accompanying table lists frequencies of leading digits from checks written by the author (an honest guy).

Table showing frequencies of leading digits 1 to 9 in check amounts, with digit 1 occurring most frequently at 83 times.

Accepted Answer

Hello. In this video we are given that the table below shows the average daily temperature in Celsius recorded at a weather station over a seven day period during the summer. We want to use a scatter plot of the data to determine the best fitting mathematical model. Now in order to create a scatter plot, we are going to use an external tool. In this case, I will be using Google Sheets, but the first thing we want to do is you want to take the data set and separate it into two different columns in Google Sheets. So let's go ahead and do that. So what I've done here is I've taken the given data set and I separated it into two separate columns. The first column is going to represent what day the data set exists in, and the second column represents the temperature with the respective day. Now in order to create the scattered plot, the first thing we're going to do is we're going to select both of the columns. Then we are going to go to insert, and we're going to click on the chart option. This will create a chart for the data set, but in order to make it a scatter plot, we will go to chart type. And we will select the scattered chart option. So now what we have in front of us is a scatter chart of the given data. Now in order to determine which model best fits the data, we are going to be using a tool called the trend line. In order to enable the trend line, we will go ahead and click on one of our data points, and we will scroll down until we find the trend line option. Clicking this will activate the trend line for the plot. And the trend line has different models that we can select from. We have linear, exponential, polynomial, which is another way of saying quadratic and logarithmic, and we are going to look through each of the four options and select the one that best fits the data set. Now we're going to start with linear, but taking a look at the linear trend line shows that the data set doesn't fit that well. Many of the points are either above or below the trend the trend line, so this won't be an option. Now if we take a look at the exponential option, this is a little bit better, but some of the points lie above or below the trend line as well, so we'll take a look at our other options. Logarithmic doesn't follow the pattern of the data set at all, so this won't be an option either. Now when we take a look at polynomial, we want to make sure that we have a degree 2 option, that way we're working with the correct coefficient of determination. But the polynomial is going to be the best fitting model because it passes through each of the data points and none of them are either slightly above or below the trend line. So polynomial is going to be the best fitting model for the data set. And with that being said, the correct option to this problem is going to be option C. Quadratic best fits the data set. 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.

Watch next