Natural Resource BiometricsSimple Linear RegressionSimple linear regression is a tool for fitting a linear line to a set of data. It is used when you want to predict the value of the "dependent variable" Y by knowing the value of the "independent variable" X.Figure 1 is an example of a data set with a regression line fit. Figure 1. Example data set with regression line fit to data. The line in the graph can be described as: where y is the dependent variable (also plotted on the y axis of the graph), x is the independent variable (plotted on the x axis of the graph). The parameters that are estimated are b0 and b1.
These parameters can be estimated using the following equations: where X_{i} and Y_{i} are the individual observation and n is the number of observations. The results of a regression are often summarized using an analysis of
variance table.
The F test is a test to determine if the regression explains more of the variation than the mean. Another statistic that is commonly used to describe a regression is the coefficient of determination R^{2} This statistic is the proportion of the observed data explained by the regression. This statistic is a value that ranges from 0 to 1 with 0 being no agreement between the regression and the data and 1 being perfect agreement between the data and the regression. Another important method of explaining the results of a regression is to plot the residuals against the independent variable. This analysis can be used to indicate that the model is misspecified and transformation required. Figure 2. Residual plot of the data. Also See: Chapter 16  Simple linear Regression pages 317330 in:

Natural Resources Biometrics by David R. Larsen is licensed under a Creative Commons AttributionShareAlike 4.0 International License . Author: Dr. David R. Larsen Created: August 17, 1998 Last Updated: September 13, 2014 