![]() 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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