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Say I have an fMRI experiment where I have a task that is suppose to measure response time, and the corresponding "activation" in the brain. I then have participants complete this task. Then I measure some variables through tests or assessments, and questionaries such as IQ, working memory, age, and years of education.

In fMRI experiments, as I am aware typically voxels (the name for the 3d fmri representation of a pixel) that remain "active" after statistical tests, while the participant completes a task, say something about how that brain region where those voxels are modulates that cognitive task.

Now, what if I want to use the variables that I measured, IQ, age, working memory, and years of education in a multiple linear regression test, with the brain activation to this task as the response variable, or dependent variable. What does this tell me?

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To put it simply, it will give you a equation (less error relative to data-set presumed to be correct equation). Depending on data-set, equation has constants value for each variables which will provides the ratio of one variable with other variables. You might find equation on similar format as this:

y = (b0 + b1.x1 + b2.x2 + b3.x3) + c

where x1 , x2 , x3 can be different characteristics (as variables which can be IQ, age, working momory, etc.) and b0 , b1, b2, b3 are the constant calculated from given data-set.

You can find exact value of y or x1 or x2 or x3 if you have exact value of other 3 variables.

Lets say, it was the data-set provided to an android/robot as in sci-fi movies; that android/robot will make it's decision based on this equation as law/fact/pattern and judge a person response time (if every other variables are known) or IQ (if every other variables are known) etc. by this equation.

There is also a lot of details in this.

Note: This logic will only practical with Multiple Linear Regression Method.

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