Manuals/calci/SLOPE

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 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.
• 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 nonnumeric. 
 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.y={0,9,4}

 x={-1,5,7}

SLOPE(C1:C3)=0.730769230769

See Also

• INTERCEPT
• RSQ
• PEARSON