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Simple Linear Regression

Implement simple linear regression using the closed-form (least squares) solution.

Given a list of $x$ values and a list of $y$ values, compute the slope $m$ and intercept $b$ of the best-fit line $y = mx + b$ .

The formulas are: $m = \frac{n\sum x_i y_i - \sum x_i \sum y_i}{n\sum x_i^2 - (\sum x_i)^2}$ $b = \bar{y} - m\bar{x}$

where $n$ is the number of data points and $\bar{x}$ , $\bar{y}$ are the means.

Return a tuple (slope, intercept), both rounded to 4 decimal places.

Input:

X = [1, 2, 3, 4, 5]
y = [2, 4, 5, 4, 5]

Output:

(0.6, 2.2)

Reasoning:

First, we calculate the necessary sums: $\sum x_i = 1 + 2 + 3 + 4 + 5 = 15$ , $\sum y_i = 2 + 4 + 5 + 4 + 5 = 20$ , $\sum x_i y_i = 1*2 + 2*4 + 3*5 + 4*4 + 5*5 = 2 + 8 + 15 + 16 + 25 = 66$ , and $\sum x_i^2 = 1^2 + 2^2 + 3^2 + 4^2 + 5^2 = 1 + 4 + 9 + 16 + 25 = 55$ .
Then, we calculate the slope $m$ using the formula: $m = \frac{5*66 - 15*20}{5*55 - 15^2} = \frac{330 - 300}{275 - 225} = \frac{30}{50} = 0.6$ .
Next, we calculate the means: $\bar{x} = \frac{15}{5} = 3$ and $\bar{y} = \frac{20}{5} = 4$ , and then the intercept $b = \bar{y} - m\bar{x} = 4 - 0.6*3 = 4 - 1.8 = 2.2$ .
The final output is a tuple of the slope and intercept, both rounded to 4 decimal places: $(0.6, 2.2)$ .

Editor

Python 3.13.1

0/0

Run code to see test results.