For example, to find out if your weight depends on the amount of calories you consume, you could lower your caloric intake (calories is the manipulated variable) for a period of time and see how your weight changes in response.
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Sometimes when a business is struggling and there is no way to know why you can use a manipulated variable to see if that is the problem.
Sometimes thing are not perfect, not everything is ideal, occasionally there exists a manipulated variable that affects the outcome of experiments.
If you wanted to find out if an action is the cause of an event you could try using a manipulated variable to see if that is what causes it.