Difference between revisions of "Manuals/calci/INTERCEPT"

Revision as of 22:23, 2 January 2014

INTERCEPT(y,x)

$y$ is the set of dependent data
$x$ is the set of independent data.

Description

This function is calculating the point where the line is intersecting y-axis using dependent and independent variables.
Using this function we can find the value of $y$ when $x$ is zero.
The intercept point is finding using simple linear regression.
It is fits a straight line through the set of $n$ points in such a way that makes vertical distances between the points of the data set and the fitted line as small as possible.
Regression methods nearly to the simple ordinary least squares also exist.
i.e.,The Least Squares method relies on taking partial derivatives with respect to the slope and intercept which provides a solvable pair of equations called normal equations.
Suppose there are $n$ data points ${y_{i},x_{i}}$ , where $i=1,2,...n$
To find the equation of the regression line: $a={\bar {y}}-b.{\bar {x}}$ .
This equation will give a "best" fit for the data points.
The "best" means least-squares method. Here b is the slope.
The slope is calculated by: $b={\frac {\sum _{i=1}^{n}{(x_{i}-{\bar {x}})(y_{i}-{\bar {y}})}}{\sum _{i=1}^{n}{(x_{i}-{\bar {x}})}^{2}}}$ .
In this formula ${\bar {x}}$ and ${\bar {y}}$ are the sample means AVERAGE of $x$ and $y$ .
In $INTERCEPT(y,x)$ , the arguments can be numbers, names, arrays, or references that contain numbers.
The arrays values are disregarded when it is contains text, logical values or empty cells.
This function will return the result as error when any one of the argument is non-numeric or $x$ and $y$ is having different number of data points and there is no data.