CADDIS Volume 4: Data Analysis
Authors: G.W. Suter II, P. Shaw-Allen, L.L. Yuan, S.M. Cormier
Linear regression is an approach for quantifying the relationship between a dependent (response) variable and an independent (explanatory) variable. The relationship is often assumed to be a straight line, but may also be curvilinear or nonlinear.
A regression tool is available in CADStat. Linear regression tools are also available in most spreadsheets and statistical programs.
After running a linear regression, most programs will provide statistics that describe the characteristics of the estimated fit to the data. These statistics include estimated values for the coefficients, the standard errors and p-values for those coefficients (see discussion of interpreting p-values), and a measure of the degree the model accounted for observed variability in the response relative to a constant, null model (R2). Several existing resources provide complete explanations for these different statistics (e.g., the Handbook of Biological Statistics ).
It is often useful to plot your data and superimpose the estimated regression line with confidence or prediction intervals (Figure 1). Confidence intervals provide an estimate of the range of possible values for the estimated mean response for any given values of explanatory variables, while prediction intervals provide an estimate of the range of possible values of the response in individual samples. In general, confidence and predictions intervals are only meaningful in cases in which regression assumptions are satisfied (see Regression Analysis: Details for more information).
Linear regression is the underlying, basic analysis on which many more advanced techniques are based. Some examples of these advanced analyses include:
- Controlling for Natural Variability
- Propensity Score Analysis
- Predicting Environmental Conditions from Biological Observations (PECBO)
Linear regression is also a key technique for describing stressor-response relationships.
Technical details for linear regression are available here.