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

Answer 1

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.