In many situations, such as prior to performing linear regression analysis, researchers want to test their data for linearity. Linearity means that two variables, "x" and "y," are related by a mathematical equation "y = cx," where "c" is any constant number. The importance of testing for linearity lies in the fact that many statistical methods require an assumption of linearity of data (i.e. the data was sampled from a population that relates the variables of interest in a linear fashion). This means that before using common methods like linear regression, tests for linearity must be performed (otherwise, the linear regression results cannot be accepted). SPSS, a powerful statistical software tool, allows researchers to observe with ease the possibility of the data arriving from a linear population. Through scatterplot testing methods, you can employ SPSS’s functions to arrive at a test of linearity.

Input your data into SPSS. You can do this manually, by entering the data in the spreadsheet entitled "data editor" that you initially see upon startup or by using the “open file” command in the “file” menu to open a SPSS data file. Put each point of data in each row, starting from the top.

Open the scatterplot menu. Go to “graphs” in the menu and choose “scatter.” A scatterplot dialog box will appear.

Choose “simple” in the scatterplot dialog box.

Construct the scatterplot. Select the variables to test for linearity in the “simple scatterplot” dialogue box. Choose the "x" and "y" variables. For tests of linearity, it does not matter which variables are chosen as “x” and “y,” but follow the standard method and let the dependent variable (the variable you have most interest in) be "y." Click on the variable in the left menu and then click on the arrow to the right, pointing to “y axis.” Repeat this for the x-variable, choosing the variable in the left menu and clicking on the arrow to the right pointing at “x axis.” Create the scatterplot by clicking “okay” in the "simple scatterplot" dialog box after entering the "x" and "y" variables.

Observe the resulting plot for linearity. Linearity is displayed by the data points being arranged in the shape of an oval. If you observe any other shape to the data, it is most likely that the population from which your data came is not linear in terms of the variables you are analyzing. Thus, if you do not observe the oval shape indicative of linearity, your data fail the test of linearity.

#### References

- “Using SPSS Syntax”; Jacqueline Collier; 2010