Difference between revisions of "Manuals/calci/SLOPE"
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*<math> y </math> is the set of dependent values. | *<math> y </math> is the set of dependent values. | ||
*<math> x </math> is the set of independent values. | *<math> x </math> is the set of independent values. | ||
| − | |||
==Description== | ==Description== | ||
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*The slope of a regression line (b) represents the rate of change in <math> y </math> as ,math> x </math> 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 | + | *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> | + | *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 | + | 1. Any one of the argument is non-numeric. |
| − | 2. x and y are empty or that have a different number of data points. | + | 2. <math>x</math> and <math>y</math> are empty or that have a different number of data points. |
==Examples== | ==Examples== | ||
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*[[Manuals/calci/RSQ | RSQ ]] | *[[Manuals/calci/RSQ | RSQ ]] | ||
*[[Manuals/calci/PEARSON | PEARSON ]] | *[[Manuals/calci/PEARSON | PEARSON ]] | ||
| − | |||
==References== | ==References== | ||
Revision as of 03:55, 30 January 2014
SLOPE(y,x)
- 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 } 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 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 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 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(y,x} ), 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 } 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 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
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}
.- 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 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}
are empty or that have a different number of data points.
Examples
1.
| 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.
| 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.
| A | B | C | |
|---|---|---|---|
| 1 | 0 | 9 | 4 |
| 2 | -1 | 5 | 7 |
=SLOPE(C1:C3) = 0.730769230769