In experiments the controlled variable is the variable which the experimenter has control of. It is also called the independent variable The dependant variable is the variable which depends on the controlled variable. The dependant variable is a random variable as we cannot predict its value before doing the experiment. Controlled Variables

Suppose we have data showing that there is a strong linear relationship between the amount of fertilizer used on some plants and the yield from the plants. The yield clearly depends on the amount of fertilizer, not the other way round. The yield is responding to the fertilizer. In this example, the yield is called the dependent, variable. Dependent and Independent Variables The amount of fertilizer used is the independent, variable. It will have been controlled in the trial from which the data have been taken.

This line is then used to estimate y from x and also x from y. Ex If the extension of a string under an increasing weight is being studied then the controlled variable is the weight and the independent variable is the extension. The regression line to predict the extension is the E on W line where ‘E’ is the extension and ‘W’ is the weight If the variable x is controlled then only the regression line y on x has a meaning. The Extension depends upon the Weight

Using a Regression Line We need to watch out for the following when using regression lines:  The fact that we can find a regression line does not mean that a change in one variable causes a change in the other.  There may be a relationship between 2 variables that is non-linear so the regression line is inappropriate.  Although we can always find a regression line, it will have no meaning if the points are scattered widely from the line.