1. Understanding Linear Regression
Kristin L. Sainani, PhD 
PM&R 
Volume 5, Issue 12, Pages (December 2013)
DOI: /j.pmrj
Copyright © 2013 American Academy of Physical Medicine and Rehabilitation Terms and Conditions

2. Figure 1
Scatter plots of 4 hypothetical samples of 100 persons; these samples come from different virtual populations in which vitamin D levels and the digit symbol substitution test score are increasingly related. (A) No relationship. (B) Weak relationship. (C) Weak-to-moderate relationship. (D) Moderate relationship.
PM&R 2013 5, DOI: ( /j.pmrj )
Copyright © 2013 American Academy of Physical Medicine and Rehabilitation Terms and Conditions

3. Figure 2
Scatter plots of the 4 hypothetical data sets with the “best fit” lines (linear regression lines) superimposed. Slopes of the lines are indicated. (A) Slope = 0. (B) Slope = 0.5 per 10 nmol/L. (C) Slope = 1.0 per 10 nmol/L. (D) Slope = 1.5 per 10 nmol/L.
PM&R 2013 5, DOI: ( /j.pmrj )
Copyright © 2013 American Academy of Physical Medicine and Rehabilitation Terms and Conditions

4. Figure 3
A 3-dimensional scatter plot of data set 4 (slopeDSST – vitamin D = 1.5), with age added as a third variable. The 3-dimensional plot is shown from 2 different angles.
PM&R 2013 5, DOI: ( /j.pmrj )
Copyright © 2013 American Academy of Physical Medicine and Rehabilitation Terms and Conditions

5. Figure 4
The “best fit” plane for data set 4, shown from one angle. Horizontal lines represent the slopes for vitamin D at fixed ages; vertical lines represent the slopes for age at fixed vitamin D levels.
PM&R 2013 5, DOI: ( /j.pmrj )
Copyright © 2013 American Academy of Physical Medicine and Rehabilitation Terms and Conditions