# Math Help - variables question

1. ## variables question

Can independent and dependent variables be interchangeable? Why or why not?

What is the meaning of a positive slope and a negative slope in a regression line. Explain with an example

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2. EXTRACT from Independent Variable

An independent variable is the variable you have control over, what you can choose and manipulate. It is usually what you think will affect the dependent variable. In some cases, you may not be able to manipulate the independent variable. It may be something that is already there and is fixed, something you would like to evaluate with respect to how it affects something else, the dependent variable like color, kind, time.

Example: You are interested in how stress affects heart rate in humans. Your independent variable would be the stress and the dependent variable would be the heart rate. You can directly manipulate stress levels in your human subjects and measure how those stress levels change heart rate.

For equations such as y = 3x – 2, the independent variable is x. The variable y is not independent since it depends on the number chosen for x.

The slope in the regression line matters only for significance of the model. If it is close to zero, then regression should not be used. The slope will be in the range of $[-1,1]$
The coefficient of determination (r-squared) should be the parameter of interest here. It will vary in the range of $[0,1]$. You want r-squared values closest to one.