Implement Simple Linear Regression

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Your question is Implement Simple Linear Regression. Start with the requirements on the right.

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Problem

At Lyft, a small analytics tool needs a basic linear regression function without using external ML libraries. Given paired numeric observations, compute the best-fit line y = mx + b using ordinary least squares.

Task

Write a function that takes two arrays, x_values and y_values, and returns the slope and intercept of the regression line.

Formal Specification

Input:
- x_values: list of numbers of length n
- y_values: list of numbers of length n
Output:
- A list [slope, intercept]
If the input lengths differ, contain fewer than 2 points, or all x_values are identical, return [].

Use the formulas:

slope = sum((xi - mean_x) * (yi - mean_y)) / sum((xi - mean_x)^2)
intercept = mean_y - slope * mean_x

Constraints

2 <= n <= 10^5
x_values.length == y_values.length for valid input
-10^6 <= x_values[i], y_values[i] <= 10^6
Return [] for invalid input or when all x_values are identical
Do not use external regression or machine learning libraries

Function Signature

def linear_regression(x_values, y_values):

Your solutionPython 3

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