Implement Linear Regression Function | Dataford Interview Questions

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Problem

Purdue University student-support analytics needs a small baseline model that estimates an outcome from one numeric measurement. Implement univariate linear regression using the ordinary least-squares solution, without using machine-learning libraries.

Given paired feature values x and target values y, compute the line y = slope * x + intercept that minimizes the sum of squared prediction errors.

Formal Specification

Implement fit_linear_regression(x, y), where x and y are nonempty lists of numbers with equal length. Return a two-element list [slope, intercept] containing floating-point values. The input guarantees that x contains at least two distinct values, so the slope is defined.

Use these formulas, where x_mean and y_mean are the respective averages:

slope = sum((x[i] - x_mean) * (y[i] - y_mean)) / sum((x[i] - x_mean)^2)
intercept = y_mean - slope * x_mean

Constraints

2 <= len(x) == len(y) <= 10^5
x and y contain integers or floating-point values
At least two values in x are different
The feature variance denominator is nonzero
Do not use external numerical or machine-learning libraries

Function Signature

def fit_linear_regression(x, y):