Content development

At the start, students seemed to view regression analysis as a rather flat structure having little texture. Essentially, their recollection seemed to consist of an unordered collection of possible methods -- model search, residual plots, anova, $\ldots$ -- each student giving prominence to one or two of these and largely ignoring the rest. It was as if one or two pieces of their previous course had stuck with them regardless of its importance or merit (e.g. one student would describe how we needed forward selection, and then a little later ``stepwise regression''). No strategic sense was present at all.

At the end of the first session, I suggested they come to the next session prepared to identify a sequence of steps which might be taken in a regression analysis. The result was a flow chart describing a process for regression analysis. It was relatively linear and prescriptive.

``What if'' questions soon showed the linear structure to be too constraining. The overly prescriptive nature became apparent when the designers imagined themselves as the users -- the putative user for whom the design had been created turned out to be non-existent. The structure was continually repaired after each assault and quickly became quite complicated containing, for example, feedback loops and many steps which could jump to a great many others. Abstractions fell away, crowded out by detail. Any sense of strategy seemed lost.

Having explored both ends of the spectrum, it seemed wise to set aside some general task areas, determine when they might be undertaken in an analysis, and ask what information should be available at that step in order to carry out the tasks. Isolating task areas and following the data led to the final strategic representation of a regression analysis shown as the directed graph of Figure 1.

  

Figure 1: Students' strategy for regression analysis.

Each node is a step, and each arc indicates potential movement from one step to another. (The arc from the ``model search'' node carries a question mark and leads nowhere because limited progress was achieved in this area.) The strategy is loose in the sense that there can be a number of activities undertaken at each node that do not involve movement to new nodes and that it is perfectly possible, given the appropriate data structure, to enter the strategy beginning at any node.