Difference between revisions of "Manuals/calci/STEYX"
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| − | <div style="font-size:30px">'''STEYX( | + | <div style="font-size:30px">'''STEYX (KnownYs,KnownXs) '''</div><br/> |
| − | *<math> | + | *<math>KnownYs</math> is set of dependent values. |
| − | *<math> | + | *<math>KnownXs </math> is the set of independent values. |
| + | **STEYX(),returns the standard error of the predicted y-value for each x in the regression. | ||
==Description== | ==Description== | ||
*This function gives the standard error of the regression, which also is known as the standard error of the estimate. | *This function gives the standard error of the regression, which also is known as the standard error of the estimate. | ||
| − | *It is calculates the standard error for the straight line of best fit through a supplied set of <math> | + | *It is calculates the standard error for the straight line of best fit through a supplied set of <math> KnownXs</math> and <math> KnownYs</math> values. |
| − | *The standard error for this line provides a measure of the error in the prediction of <math> | + | *The standard error for this line provides a measure of the error in the prediction of <math> KnownYs </math> for an individual <math> KnownXs </math>. |
*The equation for the standard error of the predicted <math> y </math> is: | *The equation for the standard error of the predicted <math> y </math> is: | ||
<math>\sqrt{\frac{1}{(n-2)}\left [ \sum(y-\bar{y})^2-\frac{[\sum(x-\bar{x})(y-\bar{y})]^2}{\sum(x-\bar{x})^2} \right ]}</math> | <math>\sqrt{\frac{1}{(n-2)}\left [ \sum(y-\bar{y})^2-\frac{[\sum(x-\bar{x})(y-\bar{y})]^2}{\sum(x-\bar{x})^2} \right ]}</math> | ||
where <math>\bar{x}</math> and <math>\bar{y}</math> are the sample mean <math> x </math> and <math> y </math>. | where <math>\bar{x}</math> and <math>\bar{y}</math> are the sample mean <math> x </math> and <math> y </math>. | ||
| − | *In <math> STEYX( | + | *In <math>STEYX (KnownYs,KnownXs)</math>, <math>KnownYs </math> is the array of the numeric dependent values and <math> KnownXs </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. | ||
*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 non-numeric. | 1. Any one of the argument is non-numeric. | ||
| − | 2. | + | 2. KnownYs and KnownXs are empty or that have less than three data points. |
| − | 3. | + | 3. KnownYs and KnownXs have a different number of data points. |
==Examples== | ==Examples== | ||
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|} | |} | ||
| − | =STEYX(A1:F1,A2:F2) = 1. | + | =STEYX(A1:F1,A2:F2) = 1.4525201161135368 |
2. | 2. | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 46: | Line 47: | ||
|} | |} | ||
| − | =STEYX(A1:E1,A2:E2)) = 5. | + | =STEYX(A1:E1,A2:E2)) = 5.944184833375669 |
3. | 3. | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 73: | Line 74: | ||
==References== | ==References== | ||
*[http://www.ncssm.edu/courses/math/Talks/PDFS/Standard%20Errors%20for%20Regression%20Equations.pdf Standard Error] | *[http://www.ncssm.edu/courses/math/Talks/PDFS/Standard%20Errors%20for%20Regression%20Equations.pdf Standard Error] | ||
| + | |||
| + | |||
| + | |||
| + | |||
| + | *[[Z_API_Functions | List of Main Z Functions]] | ||
| + | |||
| + | *[[ Z3 | Z3 home ]] | ||
Latest revision as of 13:58, 18 June 2018
STEYX (KnownYs,KnownXs)
- is set of dependent values.
- is the set of independent values.
- STEYX(),returns the standard error of the predicted y-value for each x in the regression.
is set of dependent values.
is the set of independent values.
Description
- This function gives the standard error of the regression, which also is known as the standard error of the estimate.
- It is calculates the standard error for the straight line of best fit through a supplied set of and values.
- The standard error for this line provides a measure of the error in the prediction of for an individual .
- The equation for the standard error of the predicted is:
is:where and are the sample mean and .
![{\displaystyle {\sqrt {{\frac {1}{(n-2)}}\left[\sum (y-{\bar {y}})^{2}-{\frac {[\sum (x-{\bar {x}})(y-{\bar {y}})]^{2}}{\sum (x-{\bar {x}})^{2}}}\right]}}}](https://wikimedia.org/api/rest_v1/media/math/render/png/f71cd618f3c8c4c1d1e43f8434dc9778e8b8a697)
where 
and 
are the sample mean 
and - 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.
- This function will return the result as error when
, 1. Any one of the argument is non-numeric. 2. KnownYs and KnownXs are empty or that have less than three data points. 3. KnownYs and KnownXs have a different number of data points.
Examples
1.
| A | B | C | D | E | F | |
|---|---|---|---|---|---|---|
| 1 | 6 | 8 | 10 | 13 | 15 | 5 |
| 2 | 1 | 4 | 8 | 11 | 20 | 3 |
=STEYX(A1:F1,A2:F2) = 1.4525201161135368
2.
| A | B | C | D | E | |
|---|---|---|---|---|---|
| 1 | 2 | 9 | 1 | 8 | 17 |
| 2 | 10 | 4 | 11 | 2 | 6 |
=STEYX(A1:E1,A2:E2)) = 5.944184833375669
3.
| A | B | C | D | E | |
|---|---|---|---|---|---|
| 1 | 1 | 2 | 4 | 5 | 8 |
| 2 | 10 | 4 | 7 | 5 |
=STEYX(A1:A5,B1:B4) = NAN
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References