If the independent variables are categorical or binary, then the regression coefficient must be interpreted in reference to the numerical encoding of these variables. However, such an extrapolation is generally not useful. Mathematically it is possible to estimate the weight of a person whose height is outside the range of values observed in the study. The data set need not include any person with this precise height. Linear regression can be used to estimate the weight of any persons whose height lies within the observed range (1.59 m to 1.93 m). The data set contains 6 persons whose height is 1.74 m, and their weights vary from 63 to 75 kg. kilograms).įigure 3 shows the regression line that represents the linear relationship between height and weight.įor a person whose height is 1.74 m, the predicted weight is 68.50 kg (y = –133.18 + 115.91 × 1.74 m). Special attention to this issue is needed when publications from different countries use different units to express the same variables (e.g., feet and inches vs. Proper interpretation thus requires that the regression coefficient should be considered together with the units of all of the involved variables. The constant a, in contrast, is independent of the unit chosen to express the independent variables. If height had been measured in meters, rather than in centimeters, the regression coefficient b would have been 115.91 instead. The regression coefficient of 1.16 means that, in this model, a person’s weight increases by 1.16 kg with each additional centimeter of height.

In general, only values within the range of observations of the independent variables should be used in a linear regression model prediction of the value of the dependent variable becomes increasingly inaccurate the further one goes outside this range. Therefore, interpretation of the constant is often not useful. The y-intersect a = –133.18 is the value of the dependent variable when X = 0, but X cannot possibly take on the value 0 in this study (one obviously cannot expect a person of height 0 centimeters to weigh negative 133.18 kilograms). On the basis of the data, the following regression line was determined: Y= –133.18 + 1.16 × X, where X is height in centimeters and Y is weight in kilograms. The relationship between height and weight was studied: weight in kilograms was the dependent variable that was to be estimated from the independent variable, height in centimeters. Their height ranged from 1.59 to 1.93 meters. In a fictitious study, data were obtained from 135 women and men aged 18 to 27. The following example should make this relationship clear: The proper interpretation of the regression coefficient thus requires attention to the units of measurement. If the independent variable is continuous (e.g., body height in centimeters), then the regression coefficient represents the change in the dependent variable (body weight in kilograms) per unit of change in the independent variable (body height in centimeters). It provides a measure of the contribution of the independent variable X toward explaining the dependent variable Y. The slope b of the regression line is called the regression coefficient. R-squared linear = coefficient of determination A scatter plot and the corresponding regression line and regression equation for the relationship between the dependent variable body weight (kg) and the independent variable height (m).

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