Difference between revisions of "Manuals/calci/SLOPE"
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| − | <div | + | <div style="font-size:30px">'''SLOPE (KnownYArray,KnownXArray)'''</div><br/> |
| + | *<math> KnownYArray </math> is the set of dependent values. | ||
| + | *<math> KnownXArray </math> 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 <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 co-variance of <math>x</math> and <math>y</math>, divided by the sum of squares (variance) of <math>x</math>. | ||
| + | *In <math>SLOPE (KnownYArray,KnownXArray)</math>, <math>KnownYArray </math> is the array of the numeric dependent values and <math> KnownXArray </math> 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 | ||
| + | :<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 | ||
| + | 1. Any one of the argument is non-numeric. | ||
| + | 2. <math>KnownYArray</math> and <math>KnownXArray</math> are empty or that have a different number of data points. | ||
| − | + | ==Examples== | |
| + | 1. | ||
| + | {| class="wikitable" | ||
| + | |+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. | ||
| + | {| class="wikitable" | ||
| + | |+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 | |
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| − | + | 3. | |
| + | {| class="wikitable" | ||
| + | |+Spreadsheet | ||
| + | |- | ||
| + | ! !! A !! B !! C | ||
| + | |- | ||
| + | ! 1 | ||
| + | | 0 || 9 || 4 | ||
| + | |- | ||
| + | ! 2 | ||
| + | | -1 || 5 || 7 | ||
| + | |} | ||
| + | =SLOPE(C1:C3) = 0.730769230769 | ||
| − | + | ==Related Videos== | |
| − | + | {{#ev:youtube|MeU-KzdCBps|280|center|SLOPE}} | |
| − | - | ||
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| − | + | ==See Also== | |
| + | *[[Manuals/calci/INTERCEPT | INTERCEPT]] | ||
| + | *[[Manuals/calci/RSQ | RSQ ]] | ||
| + | *[[Manuals/calci/PEARSON | PEARSON ]] | ||
| − | + | ==References== | |
| − | + | *[http://stattrek.com/regression/slope-test.aspx?Tutorial=AP Linear regression line] | |
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| − | + | *[[Z_API_Functions | List of Main Z Functions]] | |
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| − | + | *[[ Z3 | Z3 home ]] | |
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Latest revision as of 17:12, 1 August 2018
SLOPE (KnownYArray,KnownXArray)
- is the set of dependent values.
- is the set of independent values.
- SLOPE(), returns the slope of the linear regression line.
is the set of dependent values.
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 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 , divided by the sum of squares (variance) of .
- In , is the array of the numeric dependent values and 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
as ,math> x </math> changes.
and 
, 
where and are the sample mean x and y.
and 
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. and 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,A2: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
Related Videos
See Also
References