Kata

Background:

A linear regression line has an equation in the form $Y=a+bXY\; =\; a\; +\; bX$, where $XX$ is the explanatory variable and $YY$ is the dependent variable. The parameter $bb$ represents the slope of the line, while $aa$ is called the intercept (the value of $yy$ when $x=0x\; =\; 0$).

For more details visit the related wikipedia page.

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Task:

The function that you have to write accepts two list/array, $xx$ and $yy$, representing the coordinates of the points to regress (so that, for example, the first point has coordinates (x[0], y[0])).

Your function should return a tuple (in Python) or an array (any other language) of two elements: a (intercept) and b (slope) in this order.

You must round your result to the first 4 decimal digits

Formula:

$x_{i}x\_i$ and $y_{i}y\_i$ is $xx$ and $yy$ co-ordinate of $ii$-th point;
$nn$ is length of input.

$a={\displaystyle \frac{\sum x_i^2\cdot \sum y_i-\sum x_i\cdot \sum x_i{y}_i}{n\sum x_i^2-(\sum x_i{)}^2}}a\; =\; \backslash dfrac\{\backslash sum\; x\_i^2\backslash cdot\; \backslash sum\; y\_i\; -\; \backslash sum\; x\_i\; \backslash cdot\backslash sum\; x\_iy\_i\}\{n\backslash sum\; x\_i^2\; -\; (\backslash sum\; x\_i)^2\}$

$b={\displaystyle \frac{n\sum x_i{y}_i-\sum x_i\cdot \sum y_i}{n\sum x_i^2-(\sum x_i{)}^2}}b\; =\; \backslash dfrac\{n\backslash sum\; x\_i\; y\_i\; -\; \backslash sum\; x\_i\; \backslash cdot\; \backslash sum\; y\_i\}\{n\backslash sum\; x^2\_i\; -\; (\backslash sum\; x\_i)^2\}$

Examples:

regressionLine([25,30,35,40,45,50], [78,70,65,58,48,42]) == (114.381, -1.4457)

regressionLine([56,42,72,36,63,47,55,49,38,42,68,60], [147,125,160,118,149,128,150,145,115,140,152,155]) == (80.7777, 1.138)

regression_line([25,30,35,40,45,50], [78,70,65,58,48,42]) === [114.381, -1.4457]

regressionLine([56,42,72,36,63,47,55,49,38,42,68,60], [147,125,160,118,149,128,150,145,115,140,152,155]) === [80.7777, 1.138]

regressionLine([25,30,35,40,45,50], [78,70,65,58,48,42]) == [114.381, -1.4457]

regressionLine([56,42,72,36,63,47,55,49,38,42,68,60], [147,125,160,118,149,128,150,145,115,140,152,155]) == [80.7777, 1.138]

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