## Day 10: Modeling Trends in Data

#### by: BJ Jackson

Discussion

Sometimes, individuals have information relating two variables and want to be able to predict what would happen at other values. This is done by modeling. In modeling, we take data and try to fit a curve to the data points. The curve has an equation associated with it. This equation, if known or found, will then allow us to predict what happens at values that are that we do not have.

For right now, we are going to try and fit a line onto given data sets and then find the equation of the line in order to predict new values. Later, you will be asked to fit curves other than lines to different data sets.

So, to start we need a data set that relates two different values. Up until now, we have called these data sets x and y. In research, data sets come from some experiment so they are called experimental values. One example of this might be time and temperature.

Here, a person might start at 1 a.m. and use a thermometer to find the temperature. So, the person would now have a data point where the x value is time and the value is temperature. It would be in the form (time, temp). Now, the person continues to take readings every hour until 12 noon. This individual would now have 12 data points in the form of (time, temp). He/she could then plot the data in a scatter plot and put the data in a table in order to organize the data. Now, the person can find and equation that represents the relationship between time and temperature.

The following links will take give some examples of how to model data, find the equation of the line, and make predictions based on the line.

Example 1: Time and Temperature

Example 2: