# ak.linear_fit¶

Defined in awkward.operations.reducers on line 1275.

ak.linear_fit(x, y, weight=None, axis=None, keepdims=False, mask_identity=True)
Parameters
• x – one coordinate to use in the linear fit.

• y – the other coordinate to use in the linear fit.

• weight – data that can be broadcasted to `x` and `y` to give each point a weight. Weighting points equally is the same as no weights; weighting some points higher increases the significance of those points. Weights can be zero or negative.

• axis (None or int) – If None, combine all values from the array into a single scalar result; if an int, group by that axis: `0` is the outermost, `1` is the first level of nested lists, etc., and negative `axis` counts from the innermost: `-1` is the innermost, `-2` is the next level up, etc.

• keepdims (bool) – If False, this function decreases the number of dimensions by 1; if True, the output values are wrapped in a new length-1 dimension so that the result of this operation may be broadcasted with the original array.

• mask_identity (bool) – If True, the application of this function on empty lists results in None (an option type); otherwise, the calculation is followed through with the reducers’ identities, usually resulting in floating-point `nan`.

Computes the linear fit of `y` with respect to `x` (many types supported, including all Awkward Arrays and Records, must be broadcastable to each other). The grouping is performed the same way as for reducers, though this operation is not a reducer and has no identity.

This function has no NumPy equivalent.

Passing all arguments to the reducers, the linear fit is calculated as

```sumw            = ak.sum(weight)
sumwx           = ak.sum(weight * x)
sumwy           = ak.sum(weight * y)
sumwxx          = ak.sum(weight * x**2)
sumwxy          = ak.sum(weight * x * y)
delta           = (sumw*sumwxx) - (sumwx*sumwx)

intercept       = ((sumwxx*sumwy) - (sumwx*sumwxy)) / delta
slope           = ((sumw*sumwxy) - (sumwx*sumwy))   / delta
intercept_error = np.sqrt(sumwxx / delta)
slope_error     = np.sqrt(sumw   / delta)
```

The results, `intercept`, `slope`, `intercept_error`, and `slope_error`, are given as an `ak.Record` with four fields. The values of these fields might be arrays or even nested arrays; they match the structure of `x` and `y`.

See `ak.sum` for a complete description of handling nested lists and missing values (None) in reducers, and `ak.mean` for an example with another non-reducer.