How should I practice Through-Origin Linear Regression?

Start by reading the full statement, solve the visible examples, then compare the pattern against related Meta phone screen problems in FastPrep.

Is Through-Origin Linear Regression associated with Meta?

FastPrep tags this as a Meta phone screen coding practice problem when the problem catalog has that company and stage context.

Through-Origin Linear Regression

Meta● EasyNEW GRADPHONE SCREEN

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Problem statement

You are given a nonempty list of observed points points[i] = [x_i, y_i]. Fit the no-intercept model predicted_y = w * x by choosing one real-valued weight w that minimizes the mean squared error.

MSE(w) = sum((y_i - w * x_i)^2) / points.length

For this exercise, each feature and label is an integer. Repeated observations remain separate samples. Return the minimizing weight as a floating-point number. Do not fit a bias or intercept.

If every feature is zero, every weight gives the same error; return 0.0. Otherwise the minimizing weight is unique. Answers are accepted with relative-or-absolute tolerance 10^-9.

Function

fitThroughOrigin(points: int[][]) → double

Examples

Example 1

points = [[1,2],[2,4],[3,6]]return = 2.0

All observations lie on y = 2x, so the zero-loss weight is 2.

Example 2

points = [[1,3],[2,5],[3,7]]return = 2.4285714285714284

The numerator is 34 and the denominator is 14. The weight is 17/7; fitting an intercept would solve a different problem.

Example 3

points = [[0,4],[0,-3]]return = 0.0

All x values are zero, so changing the weight changes no prediction. The stated convention returns 0.

Constraints

1 <= points.length <= 10000.
Each point contains exactly two integers [x_i, y_i].
-10000 <= x_i, y_i <= 10000.
Use sufficiently wide arithmetic for products and sums; each accumulator has magnitude at most 10^12.