Difference between revisions of "Manuals/calci/SLOPE"

Revision as of 03:55, 30 January 2014

SLOPE(y,x)

$y$ is the set of dependent values.
$x$ 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 $y$ 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 $x$ 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.
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

b={\frac {\sum (x-{\bar {x}})(y-{\bar {y}})}{\sum (x-{\bar {x}})^{2}}}

where ${\bar {x}}$ and ${\bar {y}}$ 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.  $x$  and  $y$  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,B2: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

References

@@ Line 2: / Line 2: @@
 *<math> y </math> is the set of dependent values.
 *<math> x </math> is the set of independent  values.
 ==Description==
@@ Line 8: / Line 7: @@
 *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.
-*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 co-variance of <math>x</math> and <math>y</math>, divided by the sum of squares (variance) of <math>x</math>.
-*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.
+*In <math>SLOPE(y,x</math>), <math>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
-. Any one of the argument is nonnumeric.
+. Any one of the argument is non-numeric.
-. x and y are empty or that have a different number of data points.
+. <math>x</math> and <math>y</math> are empty or that have a different number of data points.
 ==Examples==
@@ Line 64: / Line 65: @@
 *[[Manuals/calci/RSQ  | RSQ ]]
 *[[Manuals/calci/PEARSON | PEARSON ]]
 ==References==

Difference between revisions of "Manuals/calci/SLOPE"

Revision as of 03:55, 30 January 2014

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Description

Examples

See Also

References

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