Understanding Linear Regression Kristin L. Sainani, PhD  PM&R  Volume 5, Issue 12, Pages 1063-1068 (December 2013) DOI: 10.1016/j.pmrj.2013.10.002 Copyright © 2013 American Academy of Physical Medicine and Rehabilitation Terms and Conditions

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, 1063-1068DOI: (10.1016/j.pmrj.2013.10.002) Copyright © 2013 American Academy of Physical Medicine and Rehabilitation Terms and Conditions

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, 1063-1068DOI: (10.1016/j.pmrj.2013.10.002) Copyright © 2013 American Academy of Physical Medicine and Rehabilitation Terms and Conditions

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, 1063-1068DOI: (10.1016/j.pmrj.2013.10.002) Copyright © 2013 American Academy of Physical Medicine and Rehabilitation Terms and Conditions

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, 1063-1068DOI: (10.1016/j.pmrj.2013.10.002) Copyright © 2013 American Academy of Physical Medicine and Rehabilitation Terms and Conditions