Linear Regression (Regression Coefficient, Correlation Coefficient and Their Standard Errors)

Abstract

Similarly to unpaired t-tests and Mann-Whitney tests (Chap. 7), linear regression can be used to test whether there is a significant difference between two unpaired treatment modalities. To understand how it works, picture a linear regression of cholesterol levels and diameters of coronary arteries. It will show that the higher the cholesterol, the narrower the coronary arteries. Cholesterol levels are drawn on the x-axis, coronary diameters on the y-axis, and the best fit regression line about the data can be calculated. If coronary artery risk is measured on the y-axis instead of coronary artery diameter, then a positive correlation will be observed. Instead of a continuous variable on the x-axis, a binary variable can be adequately used, such as two treatment modalities, e.g. a worse and better treatment. With hours of sleep on the y-axis, a nice linear regression analysis can be performed: with better sleeping treatment, larger numbers of sleeping hours will be observed. The treatment modality is called the x-variable.