Difference between revisions of "Manuals/calci/INTERCEPT"

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<div style="font-size:30px">'''INTERCEPT(y,x)'''</div><br/>
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<div style="font-size:30px">'''INTERCEPT (KnownYArray,KnownXArray)'''</div><br/>
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*<math>y</math> is the set of dependent data  
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*<math>KnownYArray</math> is the set of dependent data  
−
* <math>x</math> is the set of independent data.  
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*<math>KnownXArray</math> is the set of independent data.
 +
**INTERCEPT(),returns the intercept of the linear regression line.
  
 
==Description==
 
==Description==
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*This function is calculating the point where the line is intesecting y-axis using dependent and independent variables.
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*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 <math> y </math> when <math> x </math> is zero.
 
*Using this function we can find the value of <math> y </math> when <math> x </math> is zero.
 
*The intercept  point is finding using  simple linear regression.
 
*The intercept  point is finding using  simple linear regression.
 
*It is fits a straight line through the set of <math> n </math> points in such a way that makes vertical distances between the points of the data set and the fitted line as small as possible.
 
*It is fits a straight line through the set of <math> n </math> 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.  
 
*Regression methods nearly to the simple ordinary least squares also exist.  
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*i.e.,The Least Squares method relies on taking partial derivatives with respect to the slope  
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*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.
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and intercept which provides a solvable pair of equations called normal equations.
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*Suppose there are <math> n </math> data points <math> {y_{i}, x_{i}}</math>, where <math>i = 1, 2,...n</math>
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*Suppose there are <math> n </math> data points<math> {y_{i}, x_{i}}</math>, where i = 1, 2, …, n.
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*To find the equation of the regression line:<math> a=\bar{y}-b.\bar{x}</math>.
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*To find the equation of the regression line:<math> a=y(bar)-b.x(bar)</math>.
 
 
*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.
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*The slope is calculated by:<math> b=summation(i=1 to n)(x_{i}-x(\bar))(y_{i}-y(\bar))/ summation(i=1 to n)[(x_i-x(bar))]^2.  
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*The slope is calculated by:<math> b=\frac{\sum_{i=1}^{n} {(x_{i}-\bar{x})(y_{i}-\bar{y})}} {\sum_{i=1}^{n}{(x_{i}-\bar{x})}^2}</math>.  
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*In this formula<math> x(bar)</math> and<math> y(bar)</math> are the sample means  AVERAGE of <math> x</math>  and <math> y </math>.  
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*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>.  
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*In <math>INTERCEPT(y,x)</math> , the arguments can be numbers, names, arrays, or references that contain numbers.
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*In <math>INTERCEPT (KnownYArray,KnownXArray)</math>, 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.  
 
* The arrays  values are  disregarded when it is contains text, logical values or empty cells.  
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*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.
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*This function will return the result as error when any one of the argument is non-numeric or <math>x</math> and <math>y</math> is having different number of data points and there is no data.
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'''INTERCEPT'''('''Y''','''X''')
 
  
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'''Where Y '''is the dependent set of observations or data, and
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==ZOS==
 +
*The syntax is to calculate intercept of the regression line in ZOS is <math>INTERCEPT (KnownYArray,KnownXArray)</math>.
 +
**<math>KnownYArray</math> is the set of dependent data
 +
**<math>KnownXArray</math> is the set of independent data.
 +
*For e.g.,intercept([14,16,19,15.25],[20.1,26,10,26.4])
 +
{{#ev:youtube|ltc2nl-pwpk|280|center|Intercept}}
  
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'''Y''' is the independent set of observations or data.
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==Examples==
 +
{| class="wikitable"
 +
|+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
 +
|}
  
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</div>
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#=INTERCEPT(A1:D1,A2:D2)= 10.13265306
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----
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#=INTERCEPT(A3:E3,A4:E4)= 4.754939085
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<div id="1SpaceContent" class="zcontent" align="left">
 
  
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This function calculates  the point at which a line will intersect the y-axis using the  available x-values and y-values.
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==Related Videos==
  
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</div>
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{{#ev:youtube|LNSB0N6esPU|280|center|INTERCEPTS}}
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----
 
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<div id="7SpaceContent" class="zcontent" align="left">
 
  
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·         An array contains text, logical values, or empty cells that are ignored; but, the cells with the value zero are included.
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==See Also==
 +
*[[Manuals/calci/PEARSON  | PEARSON ]]
 +
*[[Manuals/calci/AVERAGE  | AVERAGE ]]
  
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·          INTERCEPT shows the error value, when Y and X have a dissimilar number of data points.
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==References==
 +
*[http://www.purplemath.com/modules/intrcept.htm INTERCEPT]
  
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Formulas:-
 
  
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·          The equation to calculate the intercept of the regression line, a, is:
 
  
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where b is the slope, and is calculated as:
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*[[Z_API_Functions | List of Main Z Functions]]
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and where x and y are the sample means AVERAGE(Y) and AVERAGE(X).
 
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</div>
 
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----
 
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<div id="12SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="left">
 
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INTERCEPT
 
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</div></div>
 
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----
 
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<div id="8SpaceContent" class="zcontent" align="left">
 
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Lets see an example,
 
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INTERCEPT(Y, X)
 
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'''B                        C'''
 
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10                     13
 
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8                        11
 
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15                      18
 
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6                        12
 
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12                      10
 
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<nowiki>=INTERCEPT(B2:B6,C2:C6) is 1.2268</nowiki>
 
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</div>
 
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----
 
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<div id="10SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Syntax </div><div class="ZEditBox"><center></center></div></div>
 
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----
 
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<div id="4SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Remarks </div></div>
 
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----
 
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<div id="3SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Examples </div></div>
 
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----
 
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<div id="11SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Description </div></div>
 
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----
 
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<div id="2SpaceContent" class="zcontent" align="left">
 
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{| id="TABLE3" class="SpreadSheet blue"
 
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|- class="even"
 
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| class="    " |
 
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| Column1
 
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| class="  " | Column2
 
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| class="  " | Column3
 
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| class="  " | Column4
 
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|- class="odd"
 
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| class=" " | Row1
 
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| class="sshl_f" | 10
 
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| class="sshl_f" | 13
 
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| class="sshl_f" | 1.226804
 
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| class="sshl_f" |
 
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|- class="even"
 
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| class="  " | Row2
 
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| class="sshl_f" | 8
 
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| class="sshl_f" | 11
 
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| class="SelectTD" |
 
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| class="sshl_f" |
 
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|- class="odd"
 
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| Row3
 
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| class="sshl_f" | 15
 
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| class="sshl_f" | 18
 
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| class="sshl_f" |
 
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| class="sshl_f" |
 
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|- class="even"
 
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| Row4
 
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| class="sshl_f" | 6
 
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| class="sshl_f" | 12
 
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| class="sshl_f" |
 
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| class="sshl_f" |
 
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|- class="odd"
 
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| class=" " | Row5
 
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| class="sshl_f" | 12
 
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| class="sshl_f" | 10
 
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| class="sshl_f" |
 
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| class="sshl_f" |
 
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|- class="even"
 
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| Row6
 
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| class="sshl_f" |
 
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| class="sshl_f" |
 
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| class="sshl_f" |
 
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| class="sshl_f" |
 
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|}
 
  
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<div align="left">[[Image:calci1.gif]]</div></div>
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*[[ Z3 |  Z3 home ]]
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----
 

Latest revision as of 16:04, 1 August 2018

INTERCEPT (KnownYArray,KnownXArray)


  • is the set of dependent data
  • 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 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
  • 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 non-numeric or and 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 .
    • is the set of dependent data
    • 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

References


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