3.2 No Relation
One possible outcome of an experiment is that changing the independent variable will have no effect on the dependent variable. When this happens we say that there is no relationship between the variables. The graph on the previous page is an example of an experiment that demonstrates the fact that there is no relationship between the mass of a pendulum and its period when we hold the length and amplitude constant. Since as the independent variable increases and the dependent variable stays the same, the resulting graph is a horizontal line. The slope of a horizontal line is always zero. Even though such a graph demonstrates no relationship between the variables, an equation of the line can still be determined. To the right is a sketch of a graph that shows no relationship between the period of a pendulum and its mass.
Below is a detailed example of the mathematical analysis of the graph for the Period vs. mass experiment described earlier in this document.
Most of the steps in this example should be included in the mathematical analysis of a no relation experiment. Step 2 is really not necessary except as a guide to properly setting up the equation in step 3. Steps 5 and 6 could be omitted if it is clear that the trend of the graph is a horizontal line since the slope of all horizontal lines is zero. It would be acceptable, therefore, to go directly from step 4 to step 7. All other steps are essential and should be included. If you are using the computer to generate the graph and the computer calculates the slope for you, you could also conceivably omit steps 5 and 6 if you were to indicate that the computer calculated the slope for you.