Difference between revisions of "Manuals/calci/SLOPE"

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==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.
*The slope of a regression line (b) represents the rate of change in y as x changes.  
+
*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.  
 
*Slope is  found by calculating b as the covariance of x and y, divided by the sum of squares (variance) of x.  
 
*Slope is  found by calculating b as the covariance of x and y, divided by the sum of squares (variance) of x.  
*In SLOPE(y,x), y is the array of the numeric dependent values and x is the array of the independent values.  
+
*In <math>SLOPE(y,x), y </math> is the array of the numeric dependent values and <math> x </math> is the array of the independent values.  
 
*The arguments can be be either numbers or names, array,constants or references that contain numbers.
 
*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.  
 
*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 :<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.
+
*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.
 
*This function will return the result as error when  
 
*This function will return the result as error when  
 
   1. Any one of the argument is nonnumeric.  
 
   1. Any one of the argument is nonnumeric.  

Revision as of 04:13, 20 January 2014

SLOPE(y,x)


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


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 covariance of x and y, divided by the sum of squares (variance) of x.
  • 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 nonnumeric. 
 2. x and y are empty or that have a different number of data points.

Examples

1.y={4,9,2,6,7}

x={1,5,10,3,4}

SLOPE(A1:A5,B1:B5)=-0.305309734513 2.y={2,9,3,8,10,17}

x={4,5,11,7,15,12}

SLOPE(B1:B6,C1:C6)=0.58510638297 3.y={0,9,4}

 x={-1,5,7}

SLOPE(C1:C3)=0.730769230769


See Also


References