In the 1970s, I drew buttons and flashing lights on a cardboard box, cut slots on each end, and called it a computer. You could write a question on a card, drop it into the entry slot, and it would come out the other end with the answer to your query. The catch (a doozy): I had to write the answer on the card before you dropped it into the computer, since nothing actually happened on the inside of the box.
In math class, we’ve reached the chapter on functions. Functions do the kinds of things I very much wanted to make happen inside my cardboard computer. They are all about inputs and outputs: f(x) = [something crazy like 3x + 2]. f(x) — which is a fancy way to say y — is dependent on the input of x. If you input something as “x” and only one thing is output at the other end, then it’s a function and you can happily plot x and f(x) on a graph.
The linear model that we learned about last fall in statistics is closely related to all of this (or so it seems to me). The linear model includes a slope (of a line), a y-intercept, and a relationship between dependent and independent variables. They all work together to help predict the locations of dots on a regression analysis graph. And I do love graphs.
Understanding dependent and independent variables about killed me last semester, and they’re doing a number on me again. But the cause/effect is clearer this time around. My hat’s off to everyone who has to teach stats to someone like me, someone who doesn’t know what an algebraic function is. I think this must have been the same kind of frustration as playing Mad Libs with someone who doesn’t know a noun from a verb from a postmodern platitude.
I feel triumphant in making this connection between functions and linear models (even if I still have some of it wrong). And I am excited to think about how the spatial mapping of data (as dots) and relationships (as lines and slopes) is a much stronger undercurrent than I realized. Maybe I should have known it. But I didn’t. But now I do. So that’s progress, with the slope of my own linear progression again pointed upward and onward.