Difference between revisions of "Manuals/calci/INTERCEPT"

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*This equation will give a "best" fit for the data points.  
 
*This equation will give a "best" fit for the data points.  
 
*The "best" means least-squares method. Here b is the slope.
 
*The "best" means least-squares method. Here b is the slope.
*The slope is calculated by:<math> b=\sum i=1 to n {(x_{i}-\bar(x))(y_{i}-\bar(y))}/ \ sum i=1 to n{(x_{i}-bar(x))}^2.  
+
*The slope is calculated by:<math> b=\sum_{i=1}^{n} {(x_{i}-\bar(x))(y_{i}-\bar(y))}/ \sum_{i=1}^{n}{(x_{i}-bar(x))}^2</math>.  
 
*In this formula<math> bar(x)</math> and<math> bar(y)</math> are the sample means  AVERAGE of <math> x</math>  and <math> y </math>.  
 
*In this formula<math> bar(x)</math> and<math> bar(y)</math> are the sample means  AVERAGE of <math> x</math>  and <math> y </math>.  
 
*In <math>INTERCEPT(y,x)</math> , the arguments can be numbers, names, arrays, or references that contain numbers.
 
*In <math>INTERCEPT(y,x)</math> , the arguments can be numbers, names, arrays, or references that contain numbers.

Revision as of 23:51, 18 December 2013

INTERCEPT(y,x)


  • is the set of dependent data
  • is the set of independent data.

Description

  • This function is calculating the point where the line is intesecting y-axis using dependent and independent variables.
  • Using this function we can find the value of when is zero.
  • The intercept point is finding using simple linear regression.
  • It is fits a straight line through the set of 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 data points , where i = 1, 2, …, n.
  • To find the equation of the regression line:.
  • 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:.
  • In this formula and are the sample means AVERAGE of and .
  • In , 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 nonnueric or x and y is having different number of data points and there is no data.

INTERCEPT(Y,X)

Where Y is the dependent set of observations or data, and

Y is the independent set of observations or data.


This function calculates  the point at which a line will intersect the y-axis using the  available x-values and y-values.


·         An array contains text, logical values, or empty cells that are ignored; but, the cells with the value zero are included.

·          INTERCEPT shows the error value, when Y and X have a dissimilar number of data points.

Formulas:-

·          The equation to calculate the intercept of the regression line, a, is:

where b is the slope, and is calculated as:

and where x and y are the sample means AVERAGE(Y) and AVERAGE(X).


INTERCEPT


Lets see an example,

INTERCEPT(Y, X)

B                        C

10                     13

8                        11

15                      18

6                        12

12                      10

=INTERCEPT(B2:B6,C2:C6) is 1.2268


Syntax

Remarks

Examples

Description

Column1 Column2 Column3 Column4
Row1 10 13 1.226804
Row2 8 11
Row3 15 18
Row4 6 12
Row5 12 10
Row6