# Multiple linear regression, fMRI

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?

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.