Difference between revisions of "Manuals/calci/SLOPE"

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<div style="font-size:30px">'''SLOPE(y,x)'''</div><br/>
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<div style="font-size:30px">'''SLOPE (KnownYArray,KnownXArray)'''</div><br/>
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*<math> y </math> is the set of dependent values.
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*<math> KnownYArray </math> is the set of dependent values.
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*<math> x </math> is the set of independent  values.
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*<math> KnownXArray </math> is the set of independent  values.
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**SLOPE(), returns the slope of the linear regression line.
  
 
==Description==
 
==Description==
 
*This function gives the slope of the linear regression line through a set of given points.
 
*This function gives the slope of the linear regression line through a set of given points.
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*The slope of a regression line (b) represents the rate of change in y as x changes.  
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*The slope of a regression line (b) represents the rate of change in <math> y </math> as ,math> x </math> changes.  
 
*To find a slope we can use the least squares method.  
 
*To find a slope we can use the least squares method.  
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*Slope is  found by calculating b as the covariance of x and y, divided by the sum of squares (variance) of x.  
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*Slope is  found by calculating b as the co-variance of <math>x</math> and <math>y</math>, divided by the sum of squares (variance) of <math>x</math>.  
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*In SLOPE(y,x), y is the array of the numeric dependent values and x is the array of the independent values.  
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*In <math>SLOPE (KnownYArray,KnownXArray)</math>, <math>KnownYArray </math> is the array of the numeric dependent values and <math> KnownXArray </math> is the array of the independent values.  
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*The arguments can be be either numbers or names, array,constants or references that contain numbers.
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*The arguments can be be either numbers or names, array, constants or references that contain numbers.
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*Suppose the array contains text,logical values or empty cells, like that values are not considered.  
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*Suppose the array contains text, logical values or empty cells, like that values are not considered.  
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*The equation for the slope of the regression line is :<math>b = \frac {\sum (x-\bar{x})(y-\bar{y})} {\sum(x-\bar{x})^2</math>.  where <math>\bar{x}</math> and <math>\bar{y}</math> are the sample mean x and y.
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*The equation for the slope of the regression line is  
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:<math>b = \frac {\sum (x-\bar{x})(y-\bar{y})} {\sum(x-\bar{x})^2}</math>
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where <math>\bar{x}</math> and <math>\bar{y}</math> are the sample mean x and y.
 
*This function will return the result as error when  
 
*This function will return the result as error when  
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   1. Any one of the argument is nonnumeric.  
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   1. Any one of the argument is non-numeric.  
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   2. x and y are empty or that have a different number of data points.
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   2. <math>KnownYArray</math> and <math>KnownXArray</math> are empty or that have a different number of data points.
  
 
==Examples==
 
==Examples==
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1.y={4,9,2,6,7}
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1.
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x={1,5,10,3,4}
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{| class="wikitable"
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SLOPE(A1:A5,B1:B5)=-0.305309734513
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|+Spreadsheet
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2.y={2,9,3,8,10,17}
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|-
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x={4,5,11,7,15,12}
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! !! A !! B !! C !! D!! E
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SLOPE(B1:B6,C1:C6)=0.58510638297
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|-
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3.y={0,9,4}
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! 1
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  x={-1,5,7}
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| 4 || 9 || 2 ||6 || 7
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SLOPE(C1:C3)=0.730769230769
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|-
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! 2
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| 1 || 5 || 10 || 3 || 4
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|}
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=SLOPE(A1:E1,A2:E2) = -0.305309734513
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2.
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{| class="wikitable"
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|+Spreadsheet
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|-
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! !! A !! B !! C !! D!! E !!F
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|-
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! 1
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| 2 || 9 || 3 ||8 || 10 ||17
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|-
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! 2
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| 4 || 5 || 11 || 7 || 15 ||12
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|}
  
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=SLOPE(A1:F1,A2:F2) = 0.58510638297
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3.
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{| class="wikitable"
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|+Spreadsheet
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|-
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! !! A !! B !! C
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|-
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! 1
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| 0 || 9 || 4
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|-
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! 2
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| -1 || 5 || 7
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|}
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=SLOPE(C1:C3) = 0.730769230769
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==Related Videos==
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{{#ev:youtube|MeU-KzdCBps|280|center|SLOPE}}
  
 
==See Also==
 
==See Also==
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*[[Manuals/calci/PEARSON | PEARSON ]]
 
*[[Manuals/calci/PEARSON | PEARSON ]]
  
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==References==
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*[http://stattrek.com/regression/slope-test.aspx?Tutorial=AP Linear regression line]
  
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==References==
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 +
 
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*[[Z_API_Functions | List of Main Z Functions]]
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*[[ Z3 |  Z3 home ]]

Latest revision as of 16:12, 1 August 2018

SLOPE (KnownYArray,KnownXArray)


  • is the set of dependent values.
  • is the set of independent values.
    • SLOPE(), returns the slope of the linear regression line.

Description

  • This function gives the slope of the linear regression line through a set of given points.
  • The slope of a regression line (b) represents the rate of change in as ,math> x </math> changes.
  • To find a slope we can use the least squares method.
  • Slope is found by calculating b as the co-variance of and , divided by the sum of squares (variance) of .
  • In , is the array of the numeric dependent values and is the array of the independent values.
  • The arguments can be be either numbers or names, array, constants or references that contain numbers.
  • Suppose the array contains text, logical values or empty cells, like that values are not considered.
  • The equation for the slope of the regression line is

where and are the sample mean x and y.

  • This function will return the result as error when
 1. Any one of the argument is non-numeric. 
 2.  and  are empty or that have a different number of data points.

Examples

1.

Spreadsheet
A B C D E
1 4 9 2 6 7
2 1 5 10 3 4 
=SLOPE(A1:E1,A2:E2) = -0.305309734513

2.

Spreadsheet
A B C D E F
1 2 9 3 8 10 17
2 4 5 11 7 15 12 
=SLOPE(A1:F1,A2:F2) = 0.58510638297

3.

Spreadsheet
A B C
1 0 9 4
2 -1 5 7 
=SLOPE(C1:C3) = 0.730769230769

Related Videos

SLOPE

See Also

References


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