Manuals/calci/INTERCEPT

INTERCEPT (KnownYArray,KnownXArray)

• $KnownYArray$ is the set of dependent data
• $KnownXArray$ is the set of independent data.
  • INTERCEPT(),returns the intercept of the linear regression line.

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 $INTERCEPT(KnownYArray,KnownXArray)$, 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.

ZOS

• The syntax is to calculate intercept of the regression line in ZOS is $INTERCEPT(KnownYArray,KnownXArray)$.
  • $KnownYArray$ is the set of dependent data
  • $KnownXArray$ is the set of independent data.
• For e.g.,intercept([14,16,19,15.25],[20.1,26,10,26.4])

Intercept

Examples

Spreadsheet

	A	B	C	D	E
1	4	5	2	10
2	12	20	15	11
3	25	-12	-9	30	18
4	10	15	-40	52	36

1. =INTERCEPT(A1:D1,A2:D2)= 10.13265306
2. =INTERCEPT(A3:E3,A4:E4)= 4.754939085

Related Videos

INTERCEPTS

See Also

• PEARSON
• AVERAGE

References

• INTERCEPT

• List of Main Z Functions

• Z3 home