Describe the Prediction, Not the Machinery
A decision-maker needs to know what a model is being asked to predict, what information it uses, and what its output means in the business process. Naming a model family alone does not answer those questions. A description such as “we used a boosted model” may be technically recognizable, but it does not tell a reader whether the output is a dollar amount, a probability, or a category—or which facts about a case went into it.
A useful plain-language account follows the prediction from inputs to output. It states what is known when the prediction is made, which future outcome is being estimated, and the period covered. It then explains the basic calculation or decision steps in terms a reader can follow. This is a description of the model’s prediction process, not a claim that its predictions are always correct or that its inputs cause the outcome.
For a decision-ready description, be precise about four things:
- Case: What is one prediction about—for example, one shipment or one customer account?
- Inputs: What information is supplied, and when is it available?
- Target and horizon: What event or amount is predicted, and over what future period?
- Output: Is the result a predicted amount, a probability, a count, or a category? What are its units?
The report should also identify important boundaries. If a model was designed for a defined population or set of input values, do not describe it as though it automatically applies to every case. A careful explanation distinguishes information available at prediction time from information that becomes known later. It also avoids turning an association in the model into a causal claim.
A Simple Additive Prediction Rule
One transparent kind of fitted model forms a numeric prediction by adding a starting value to contributions calculated from the inputs. For a fitted linear prediction rule with numeric inputs \(x_1,\ldots,x_p\), the output is:
Here, \(b_0\) is the fitted starting value and each \(b_j\) is a fitted weight associated with input \(x_j\). This expression applies to a model that actually uses this additive form; it is not a universal description of every model. Inputs must use the same units and coding that the fitted model expects.
Why does this calculation describe the prediction? The fitted rule represents its output as a starting value plus one weighted contribution for each input. For a particular case, the input values are substituted into that rule. The resulting contributions are added to the starting value, so the calculated sum is the model’s output for that case. This explains how to apply the rule; it does not establish that the weights are causal effects or that the prediction will equal the future outcome.
In a report, the symbols can be translated into operational language. Instead of showing only an equation, name each input, state its units, and show how its value contributes to the output. If the model uses a different form—such as a sequence of questions or a probability output—describe that actual process rather than forcing it into an additive explanation.
Worked Example: Estimating a Service Cost
A hypothetical equipment service team uses a fitted additive model to estimate a customer’s total service cost in dollars during the next 90 days. The model’s scoring rule is \(\widehat{y}=25+9n+1.5a\), where \(n\) is the number of service visits recorded in the previous year and \(a\) is the equipment’s age in months. At the time of scoring, a unit has \(n=4\) recorded visits and is \(a=18\) months old. Describe and calculate the prediction.
Method. Substitute the case’s recorded inputs into the supplied fitted rule, keeping the input definitions and units explicit.
The starting value is 25 dollars. The recorded visit count contributes \(9(4)=36\) dollars. The age in months contributes \(1.5(18)=27\) dollars. Therefore:
The model’s prediction is $88 for total service cost over the next 90 days. The output is a predicted amount for this case, not a bill already incurred and not a guarantee that the actual cost will be $88.
Plain-language description: “For each unit, the model uses its recorded service-visit count and equipment age to estimate total service cost in dollars over the following 90 days. For this 18-month-old unit with four recorded visits, its estimate is $88.”
Common mistake avoided. Applying the age input as 18 years would substitute a value in the wrong unit. The model expects 18 months, not \(18\times12=216\) months. The supplied input must be recorded in the units used by the fitted rule.
Explain Probability Outputs Precisely
A probability output describes the model’s estimate for a defined event over a defined period. Name the event in full: “late delivery within the next seven days” is clearer than “risk.” State whether the output is expressed as a proportion or a percentage, and do not confuse it with a count or a yes-or-no result.
The calculation behind a probability may be more involved than a simple addition. If the fitted rule in a report is explicitly an additive probability rule, it can be described and checked as such. Its range and use must be respected: a probability is between 0 and 1, and a supplied rule should only be applied in the domain for which it is intended. For other model forms, describe the output supplied by the model rather than implying that the same arithmetic applies.
Worked Example: Estimating the Probability of a Late Delivery
A hypothetical distributor uses a fitted scoring rule to estimate the probability that a shipment will arrive late within seven days of its scheduled delivery date. The supplied rule is \(\widehat{p}=0.05+0.04o+0.03r\), where \(o\) is the number of open orders associated with the shipment and \(r=1\) if it is a rush shipment and \(r=0\) otherwise. This rule is intended for \(o\) values from 0 through 5. A shipment has three open orders and is a rush shipment. Calculate and explain its output.
Method. Encode the rush indicator as specified, substitute both inputs, and express the resulting probability as a percentage.
Here, \(o=3\) and \(r=1\). The open-order contribution is \(0.04(3)=0.12\); the rush-shipment contribution is \(0.03(1)=0.03\). Adding the starting value gives:
The result \(0.20\) is a probability of 20% for the defined event and period: arriving late within seven days of the scheduled delivery date. This is the model’s estimate for this shipment, not a statement that the shipment is already late.
Common mistake avoided. The indicator is coded as 1 for a rush shipment, not as the word “rush” or the shipment’s number of open orders. Also, the output is \(0.20\), or 20%, not 0.20%. The inputs are within the stated range, so the supplied rule is being applied within its stated domain.
Describe Rule-Based Decisions in Plain Language
Some fitted models can be represented as a short sequence of questions. In a report, those questions can often be stated directly without naming the algorithm. Say what value is checked at each step, what happens for each answer, and which output is reached. The explanation should match the model’s actual rules; it should not simplify away a condition that changes the result.
Worked Example: Forecasting Next Week’s Product Demand
A hypothetical retailer uses a fitted rule to estimate next week’s demand for each item. The rule is: first, if the average weekly sales over the last four weeks are below 10 units, predict 8 units. Otherwise, if a promotion is scheduled for next week, predict 16 units. If neither condition applies, predict 12 units. The average for one item is 11.5 units, and no promotion is scheduled. State the model’s prediction and describe the steps.
Method. Apply the questions in their stated order. The first condition is checked before the promotion condition.
The four-week average is 11.5, which is not below 10 because \(11.5 \geq 10\). The first rule therefore does not produce a prediction. The promotion condition is then checked. No promotion is scheduled, so that condition also does not produce a prediction of 16. The final rule applies, giving a prediction of 12 units for next week.
Plain-language description: “The model first checks whether recent average weekly sales are below 10 units. If not, it checks whether a promotion is planned for next week. For this item, recent sales are above the cutoff and there is no planned promotion, so the model estimates demand of 12 units.”
Common mistake avoided. The cutoff is “below 10,” not “10 or below.” If the four-week average had been exactly 10, the first condition would still not apply. Also, checking the promotion condition first would not faithfully describe the stated order when the first condition is met.
What a Clear Model Description Does Not Claim
Describing the prediction process is not the same as explaining how well the model performs. It is also not a reason to make claims about why an outcome occurs. A model’s use of an input means that the input helps determine the model’s output under its fitted rule. It does not, by itself, establish that changing the input would change the real-world outcome.
For example, if a cost model uses prior service visits, a report may state that the recorded visit count is one of the model’s inputs. It should not say that an additional visit causes a specified increase in future cost unless that causal conclusion is supported by an appropriate design and analysis. Use language such as “the model uses,” “the prediction incorporates,” or “the rule assigns a contribution,” rather than “the input causes.”
A useful final check is whether a reader can answer these questions after reading the description:
- What is one prediction about?
- What is the model predicting, and over what period?
- Which inputs are used, and what do their values and units mean?
- What does the output represent, and what should it not be mistaken for?
- Are any limits on the population, input values, or timing made clear?
A concise, accurate description of those points is more informative to a decision-maker than an unexplained algorithm label. It is also aligned with the SOA Exam PA (Predictive Analytics) syllabus, which emphasizes communicating predictive analysis in a useful and responsible way.
Check Your Understanding
For each situation, identify what is being predicted, apply the stated rule, and phrase the result with its units or meaning.
- A hypothetical repair model predicts next-month cost in dollars using \(\widehat{y}=30+5v+2m\), where \(v\) is the number of visits in the prior six months and \(m\) is the machine age in months. A machine has \(v=2\) and \(m=10\). What is the prediction? (Answer: $60 for next month.)
- A hypothetical model estimates the probability of a missed appointment using \(\widehat{p}=0.06+0.02c+0.04r\), where \(c\) is the number of prior cancellations and \(r=1\) for a reminder message, 0 otherwise. For \(c=3\) and \(r=0\), calculate and describe the output. (Answer: \(0.12\), or 12%, estimated probability of a missed appointment.)
- A demand rule predicts 5 units if recent average sales are below 8; otherwise, it predicts 9 units if a promotion is planned, and 7 units if no promotion is planned. Recent average sales are exactly 8 units, and a promotion is planned. What prediction applies, and why? (Answer: 9 units; 8 is not below 8, so the promotion condition applies.)
- A fitted model uses equipment age measured in months, but a report writer enters 3 years as the value 3. What is the correct input and what reporting error occurred? (Answer: Use 36 months; the input was entered in years rather than the required unit of months.)
- A model uses the number of prior complaints to predict the probability of a future service delay. A report says, “Each additional complaint causes the delay probability to rise.” What is the problem with this description, and what is a safer alternative? (Answer: It makes an unsupported causal claim; say that the model uses prior complaint count when estimating delay probability.)