A partial dependence curve of predicted electricity demand against outdoor temperature is U-shaped — what does that tell you?
answer
- shape, not strength
- one direction cannot describe it
- heating left, cooling right
- an average over many per-row curves
- check density under the arms
basics
~20 sThe model has learned a non-monotone relationship: average predicted demand is highest at cold temperatures and at hot temperatures, and lowest in between. The curve summarises the model's average behaviour over the whole dataset, not any single building.
solid answer
~50 sA U-shaped partial dependence curve says that, averaged over every row in the data, the model predicts high demand when it is cold, falls to a minimum somewhere in the mild range, and rises again as it gets hot — heating on the left arm, cooling on the right. Two things follow. First, the model has captured a non-monotone relationship, so any summary that reports one direction or one slope for temperature would report roughly nothing. Second, the curve is an average of one curve per row, so individual buildings can be far steeper, flatter or shaped differently than the picture. It also describes the model, not the world: it shows what this model does with temperature, not what would happen if temperature were changed. Read the arms with data density in mind — the far ends usually rest on very few observations.
go deeper
Be ready to read the shape aloud: two rising arms with a minimum in the middle means the model predicts more demand when it is cold and when it is hot. Say clearly that the y-axis is an average prediction.
Explain why a single slope or coefficient would summarise this curve as almost nothing, and state that each plotted point is the mean prediction over all rows with temperature fixed at that value.
Show that you check how many observations sit under each arm before trusting the extremes, and that you would inspect per-row curves before promising the average shape holds for any individual site.
Own the reporting standard: decide what a curve like this may and may not be used to claim in a stakeholder deck, and make the caveat travel attached to the picture rather than living in the analyst's head.
## What the picture is A **partial dependence curve** shows how a trained model's *average* prediction changes as one input feature is swept across a range of values, with everything else in the data left as it is. The x-axis is the feature — here outdoor temperature. The y-axis is an **average prediction** — here predicted electricity demand — not an observed value, not an error, and not a coefficient. A **U shape** therefore reads as: at the cold end the model predicts high demand, the prediction falls as temperature rises, reaches a minimum somewhere in the mild middle, and climbs again toward the hot end. In a demand model that is exactly the physical story you would hope to see: heating load produces the left arm, cooling load produces the right arm, and the minimum sits in the comfort band where neither runs hard. ## Why the shape itself is informative The first thing the curve rules out is a **monotone summary**. If someone asks "is temperature positively or negatively related to demand in your model?", the honest answer for a U shape is "neither — it depends where you are on the axis". A model that could only express one straight-line direction for temperature would fit a nearly flat line through this pattern, because the two arms pull in opposite directions and cancel. Seeing the U is direct evidence that the model has capacity for non-monotone structure: a tree ensemble, splines, an explicit squared term, or an interaction that switches sign. The second thing it tells you is roughly **where the minimum sits** and **how asymmetric the arms are**. If the right arm is much steeper than the left, the model believes cooling drives demand harder per degree than heating does. That is a claim you can sanity-check against domain knowledge, and disagreement is a useful signal that something upstream is wrong. ## Three things the curve does not say **It is not the raw data.** The curve is not "average demand observed on days at this temperature". It is produced by running the model, and only the model. If the model is badly fit, the curve faithfully reports a badly fit model. **It is not a statement about any one building.** A partial dependence curve is a pointwise average across rows. A campus with no air conditioning may have no right arm at all, and a data centre may have a right arm three times as steep, and both are compatible with the same average U. If you care about that spread, you look at the individual per-row curves behind the average rather than the average alone. **It is not a promise about intervention.** The curve describes the model's association between the input and its output, learned from historical data. Reading the minimum as "set thermostats here and demand will drop to this level" is a different and much stronger claim than the plot supports. ## Reading it responsibly Two habits separate a careless reading from a careful one. *Check the data density under the curve.* Most plots of this kind are drawn with a rug or decile marks along the x-axis showing where the observations actually are. Extreme cold and extreme heat are usually thin, so the ends of both arms are the least supported part of the picture — the model is being asked about conditions it barely saw. *Check the y-axis range.* A U shape with a total swing of two units on a scale where predictions span two thousand is visually dramatic and practically irrelevant. Shape tells you the form of the dependence; the vertical range tells you whether it matters. Interviewers like this question because a weak candidate describes only the shape and never mentions the magnitude. ## The short version A U-shaped partial dependence curve for temperature says the model predicts more demand at both extremes and least in the middle, on average across the data. It is a statement about the model's average behaviour, it says nothing about the spread across individual rows, and it is least trustworthy exactly where the arms are most dramatic.
- Could an ordinary linear regression with only a linear temperature term produce this curve?No. For a model that is linear in that feature, sweeping the feature moves every row's prediction by the same slope, so the partial dependence curve is a straight line with exactly that slope. A U shape needs a model that can bend: an explicit squared term, splines, a tree ensemble, or an interaction that changes sign across the range.
- How much would you trust the far ends of both arms?Less than the middle. The grid usually spans the observed range, and the extreme cold and extreme hot ends typically contain very few observations, so the model is reporting behaviour it had little evidence to learn. I plot a rug or decile ticks under the axis and say plainly where the curve becomes extrapolation.
- The curve swings by only a few units — does the shape still matter?Shape and magnitude are separate readings. A clean U with a tiny vertical range means the model has learned the right form of dependence but leans on the feature very little. Always quote the y-axis swing next to the shape, otherwise a visually striking plot gets sold as an important driver.
It is the model's answer to "what do you predict at each temperature, on average across everything you have seen" — a weather-response profile, not a forecast for one building.
saying these in an interview costs you the question
- Reads the curve as observed average demand per temperature
- Says the model is broken because the relationship is not monotone
- Assumes every building follows the same U shape
- Reads the minimum as what would happen if temperature were changed
- Describes the shape without ever mentioning the y-axis range