Defining a simple linear regression of reaction times against stimulus number I have reaction times for each of nine stimuli (the stimuli being the numbers 1 to 9), all 9 variables being arranged as columns, and with subjects across rows. I would like to regress those scores (Y) against their respective numbers (X), but have trouble understanding how to define this regression in my stats package (Statistica), whose help suggests that each of the two variables (X and Y) should be selected from the variables list. X in my case would just be the numbers 1 to 9, whereas Y would be each of the 9 columns (variables).
How should this simple regression be defined? Should it be a special type of regression given that the X variable is really categorical rather than continuous? Thanks!
 A: Since you've confirmed my interpretation, here's how I'd arrange the data as per my comment:\begin{array}{rcl}\rm Subject\ ID&X&Y\\\hline1&1&Y_{1,1}\\1&2&Y_{1,2}\\&...\\2&1&Y_{2,1}\\&...\\n&9&Y_{n,9}\end{array}‌​Your $X$ is nested within subjects. With a hierarchical linear model, you can control subject variance in $Y$ that's unrelated to $X$ and also estimate whether $X$ relates to $Y$ differently for different subjects (i.e., model individual differences as a moderator, effectively). I've never used Statistica before, but it looks like StatSoft covers the details well; see Basic Example 5: Mixed-Model Nested ANOVA Design.
If $X$ is ordered (e.g., $1<2<...<9$), you might also want to consider penalized regression, which I've described in previous posts. I'm not certain the penalization method can smooth ordinal dummy coefficients in a multilevel model, but I also don't see why not. The motivation would be to reduce overfitting of big differences among adjacent levels of $X$, as may arise due to sampling error.
