Basic Linear Regression Function | Dataford Interview Questions

Write a function that fits a basic simple linear regression model using ordinary least squares. Given paired training data x and y, compute the best-fit line y = m*x + b, then use it to predict outputs for a list of query values.

Formal Specification

Implement a function that takes:

x: a list of numbers representing the independent variable
y: a list of numbers representing the dependent variable
queries: a list of numbers to predict

Return a list of predicted values for each query, using the fitted line.

Use the least-squares formulas:

m = sum((xi - mean_x) * (yi - mean_y)) / sum((xi - mean_x)^2)
b = mean_y - m * mean_x

If all x values are identical, the slope is undefined. In that case, return the mean of y for every query.

Constraints

2 <= len(x) == len(y) <= 10^5
1 <= len(queries) <= 10^5
-10^9 <= x[i], y[i], queries[i] <= 10^9
Use ordinary least squares, not iterative optimization

Function Signature

def fit_linear_regression(x, y, queries):

Your question is Basic Linear Regression Function. Start with the requirements in the Question tab.

Run and submit as often as you like. When you're ready, talk me through your approach or go straight to the code.

Problem