Response Model Lab
Name the shape, pick the form, then turn the parameters by hand until the error stops falling. This is the exercise regression automates two weeks from now.
Overview & Learning Objectives
A response model says how a marketing input turns into a market outcome. Building one is four decisions, and only the last is arithmetic: what shape do you believe the relationship has, which equation can express that shape, what values should its parameters take, and how will you judge one set of values against another.
By the end of this lab you should be able to:
- Recognise the eight response shapes from a business description, before seeing data.
- Choose among the three workhorse forms on theoretical grounds rather than fit.
- Calibrate parameters by hand against an explicit loss function.
- Explain why MAE and MSE can prefer different parameters, and which one your situation calls for.
Marketing Scenarios
Or upload your own data
Two numeric columns: the marketing input first, the outcome second. A header row is expected and is used to label the axes.
Drop a CSV here or
Step 1Name the shape you expect
Read the scenario above and commit to a shape before you look at the scatter. Choosing the form because it happened to fit best is not a theoretical justification, and it is how overfitting starts.
Steps 2 & 3Pick a form, then calibrate it
Parameters
The automatic search minimises whichever loss is selected above. Run it once under each loss and compare the parameters it lands on.
Where the model is wrong
A loss value is one number for the whole curve. The residual plot shows where the misses are. Structure here — a run of points all above the line, or a U shape — means the form itself is wrong, and no amount of parameter tuning will fix it.
Compare the three forms
Each form is fitted to the current scenario under the selected loss. Fit is not the only criterion: a form that fits marginally better but cannot respect a ceiling, or that bends violently outside the observed range, is usually the worse choice.
Exploratory Questions
- Fit the TV reach scenario with a linear model, then read the prediction at 2,000 GRPs. What does it claim, and why is that impossible?
- On the email frequency scenario, fit a linear model and then a power series. What does the linear model recommend about send frequency, and what does it miss?
- Pick any scenario. Fit it once minimising MAE and once minimising MSE. Where do the two curves differ most, and which points explain the difference?
- Add an extreme point to a scenario by uploading a modified CSV. Which loss function moves further, and what does that tell you about using MSE when your data contains genuine outliers?
- The trade promotion scenario keeps rising across the observed range. Would you still choose a form with a ceiling? What would you need to know to decide?