How is a linear relationship different from a nonlinear/curvilinear relationship?
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A linear relationship is different from a nonlinear/curvilinear relationship because a linear relationship has direct proportionality that causes the dependent variable to change when the independent variable changes, whereas a nonlinear/curvilinear relationship does not have proportionality between the dependent and independent variables (there is not consistent change). In other words, in a linear relationship all the points on the scatter diagram tends to lie near a straight line, while the points in a nonlinear/curvilinear relationship are depicted graphically by anything other than a straight line.
Example / Application
Example: Linear relationship graph and table
Application: On this web page, the linear relationship can be seen through the increase in the independent variable (number of pounds of the apples) which causes a proportional increase in the dependent variable (cost). This linear relationship can also be seen on the graph, the best-fitting regression line is a straight line.
Example: Nonlinear relationship
Application: In the video that explains how to interpret a nonlinear relationship, a nonlinear relationship is explained and shown on a graph. Although it is not easy, or perhaps even possible, to predict changes in the dependent variable based on the changes in the independent variable, using a graph to illustrate this relationship helps the researcher to interpret the results.