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What is the general formate for the equation of a least-squares regression line?

Answer 1

Liam Burke

Equation for least-squares linear regression:

#y = m x + b#

where # m = (sum(x_iy_i) - (sum x_i sum y_i)/n)/(sum x_i^2 -((sum x_i)^2)/n)#

and #b = (sum y_i - m sum x_i)/n#

for a collection of #n# pairs #(x_i,y_i)#

This looks horrible to evaluate (and it is, if you are doing it by hand); but using a computer (with, for example, a spreadsheet with columns :#y, x, xy, and x^2#) it isn't too bad.

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Answer 2

Hailey Anderson

The general format for the equation of a least-squares regression line is (y = mx + b), where:

(y) represents the dependent variable you're trying to predict,
(m) is the slope of the line, indicating the change in (y) for a one-unit change in (x),
(x) is the independent variable used to predict (y), and
(b) is the y-intercept, representing the value of (y) when (x = 0).

In the context of least squares regression, (m) and (b) are determined so as to minimize the sum of the squares of the differences between the observed values and the values predicted by the model.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.