Calculating Simple Linear Regression

Simple linear regression is a procedure that provides an estimate of the value of a dependent variable (outcome) based on the value of an independent variable (predictor). Knowing that estimate with some degree of accuracy, we can use regression analysis to predict the value of one variable if we know the value of the other variable (Cohen & Cohen, 1983). The regression equation is a mathematical expression of the influence that a predictor has on a dependent variable, based on some theoretical framework. For example, in Exercise 14, Figure 14-1 illustrates the linear relationship between gestational age and birth weight. As shown in the scatterplot, there is a strong positive relationship between the two variables. Advanced gestational ages predict higher birth weights.

A regression equation can be generated with a data set containing subjects’ x and y values. Once this equation is generated, it can be used to predict future subjects’ y values, given only their x values. In simple or bivariate regression, predictions are made in cases with two variables. The score on variable y (dependent variable, or outcome) is predicted from the same subject’s known score on variable x (independent variable, or predictor).

Research Designs Appropriate for Simple Linear Regression

Research designs that may utilize simple linear regression include any associational design (Gliner et al., 2009). The variables involved in the design are attributional, meaning the variables are characteristics of the participant, such as health status, blood pressure, gender, diagnosis, or ethnicity. Regardless of the nature of variables, the dependent variable submitted to simple linear regression must be measured as continuous, at the interval or ratio level.

Statistical Formula and Assumptions

Use of simple linear regression involves the following assumptions (Zar, 2010):

Normal distribution of the dependent (y) variable

Linear relationship between x and y

Independent observations

No (or little) multicollinearity

Homoscedasticity