Linear Regression

Summary

A regression analysis provides us with the ability to mathematically model the data we collect in lab. In turn, this allows us to make predictions about the results of additional experiments. Blindly accepting the results of such an analysis without carefully examining the data and the model, however, can lead to serious errors.

By now, you know that Data Set 1 can be explained adequately using the model

Y = 0.500*X + 3.00

although there appears to be substantial
uncertainty in the values for X, for Y, or for both X and Y. The data
in Data Set 2 are nonlinear and adequately modeled using the following
2^{nd}-order
polynomial equation

Y = -0.1276*X^{2} + 2.7808*X - 5.9957

with an R^{2} of 1. With
the exception of one data point, which appears to have an unknown source
of determinate error,
the data in Data Set 3 are linear. Removing this data point (X = 13.00,
Y = 12.74) and fitting a linear trendline gives the following model equation

Y = 0.3454*X + 4.0056

with an R^{2} of 1.

Additional information on the topics covered in this module is available using the link on the left for further study, or return to the Data Analysis home page to explore other modules.