When x-coordinates (abscissae) are evenly spaced, the least-squares linear regression matrix simplifies dramatically. The intercept equals the plain mean of y values, and the slope is a weighted sum with arithmetic weights using the formula q = 12/(m³ - m). This eliminates the need for matrix solvers entirely. The post derives this from first principles using the normal equations, demonstrates it with NumPy examples, and provides a compact Python routine `linear_fit_equal_spacing` that computes slope and offset with a simple loop — useful for embedded or resource-constrained environments where matrix libraries may be unavailable.
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