# Regression — practical usage
The `Regression` wrapper builds a **sequence of models** (*steps*). Start with a baseline, then call `next([...])` to add more predictors. Interaction terms are supported via the **`'X*Z'`** notation.
```ts
new Regression(data, { yName: string, xNames?: string[], type?: 'linear'|'logistic' })
reg.next(newPredictors: string[]): this
reg.steps: Array // each step is a fitted model
reg.results: Array> // array of .result from each step
reg.htmlTables: string // combined HTML of all steps
```
## A) Linear — baseline, then moderator (interaction)
```js
import { Analyze } from 'als-statistics';
const { Regression } = Analyze;
const data = { X:[1,2,3,4,5], Z:[0,1,0,1,0], Y:[2,3,6,7,10] };
// Step 0: Y ~ X
const reg = new Regression(data, { yName:'Y', xNames:['X'], type:'linear' });
// Step 1: add moderator Z and interaction X*Z
reg.next(['Z', 'X*Z']);
const step0 = reg.steps[0].result; // { step, n, Variable[], Coefficient[], StdError[], pValue[] }
const step1 = reg.steps[1].result; // includes the 'X*Z' row
console.log(step1.Variable.includes('X*Z')); // true
```
## B) “Mediator‐like” step (add M, compare steps)
There’s **no built-in mediation test** (Sobel/bootstrapping).
However, you can *model* a putative mediator by adding it as a predictor on the next step and comparing coefficients/R².
```js
const data = { X:[1,2,3,4,5,6], M:[2,4,5,7,7,9], Y:[3,5,7,9,10,13] };
// Step 0: Y ~ X
const reg = new Regression(data, { yName:'Y', xNames:['X'], type:'linear' });
// Step 1: Y ~ X + M
reg.next(['M']);
console.log(reg.steps[0].r2, reg.steps[1].r2); // change in R²
console.log(reg.steps[1].result.Variable.includes('M')); // true
```
## C) Logistic — classification with accuracy
```js
const data = { X:[0,1,2,3,4], Y:[0,0,0,1,1] };
const logit = new Regression(data, { yName:'Y', xNames:['X'], type:'logistic' });
const s0 = logit.steps[0];
console.log(s0.result.Accuracy); // in [0,1]
console.log(s0.predict(s0.X)); // -> [0/1,...]
console.log(s0.predictProba(s0.X)); // -> probabilities in [0,1]
```
### Notes & tips
- If you omit `xNames`, the wrapper uses **all columns except `yName`** as predictors.
- `next([...])` creates a **clone** of the previous step’s columns and (if a name contains `'*'`) generates the interaction term by multiplying the two source predictors element-wise.
- Linear steps expose `StdError[]` and `pValue[]`. Logistic steps expose `Accuracy`.
- The wrapper and cores are **deterministic** for the same inputs.