Manuals/calci/SLOPE

SLOPE (KnownYArray,KnownXArray)

• $KnownYArray$ is the set of dependent values.
• $KnownXArray$ 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 $y$ 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 $SLOPE(KnownYArray,KnownXArray)$, $KnownYArray$ is the array of the numeric dependent values and $KnownXArray$ 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. $KnownYArray$ and $KnownXArray$ 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

• INTERCEPT
• RSQ
• PEARSON

References

• Linear regression line

• List of Main Z Functions

• Z3 home