# Linear Regression

Objective: To analyze paired data by first finding means, variances, standard deviations, and covariance. Then to use these statistical measures to find the best fitting line for the set of data and the correlation coefficient of the two variables.

## Lesson:

This lesson focuses on data involving two variables and the extent to which those variables are related. It is an important mathematical topic since analyzing paired data in this way and researching links between various factors can be crucial to making decisions in medicine, business, politics, sports, and many other areas of society.

On this page, I have provided a couple data sets that I found and downloaded from the Internet. Keep in mind, however, that those are only a few samples and that exploring the Internet yourself to find data that interests you would be another good learning experience. There are countless sources from which to obtain real-world data, if not through the Internet or texts and periodicals, then through your own surveys or the use of a Calculator Based Laboratory, such as with a Vernier Motion Detector, in your own classroom.

The primary set of data, however, that this lesson will work with, is that which is input by users. You will be asked to enter up to 20 paired values at a time of the foot length and height of a person. Then, you will be able to submit your data to a server. Soon thereafter you can download an Excel file that will contain a chart of your data as well as all other data that has been sent in by users. This file will also show scatterplots of both your individual set of data and the compiled data. Looking at these charts and graphs, you can begin a regression analysis and a search for the best fitting line through the data points on each graph.