Linear Regression From Scratch | Dataford Interview Questions

Write a function that fits a univariate linear regression model from scratch. Given training data x and y, return the slope and intercept of the best-fit line y = m*x + b using least squares.

Your function must not use machine learning libraries. You may use only basic Python and math if needed.

Formal Specification

Implement: fit_linear_regression(x, y)

x: list of numeric feature values
y: list of numeric target values
Return: a tuple (m, b) where m is the slope and b is the intercept

Use the closed-form least squares solution. Assume x and y have the same length and contain at least 2 points.

If every x value is identical, the slope is undefined. In that case return (0.0, mean(y)), a horizontal line through the average of y.

Results are compared with a tolerance of 1e-6, so you do not need to round.

Constraints

2 <= len(x) <= 10^5
len(x) == len(y)
-10^6 <= x[i], y[i] <= 10^6
If all x[i] are equal, return (0.0, mean(y))
Return floating-point values for slope and intercept

Function Signature

def fit_linear_regression(x, y):

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