Manuals/calci/SLOPE

SLOPE (KnownYArray,KnownXArray)

• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KnownYArray } is the set of dependent values.
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y} , divided by the sum of squares (variance) of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} .
• In Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle SLOPE (KnownYArray,KnownXArray)} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KnownYArray } is the array of the numeric dependent values and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b = \frac {\sum (x-\bar{x})(y-\bar{y})} {\sum(x-\bar{x})^2}}

where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \bar{x}} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KnownYArray}
 and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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