Difference between revisions of "Manuals/calci/RSQ"
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| − | <div style="font-size:30px">'''RSQ( | + | <div style="font-size:30px">'''RSQ (Array1,Array2)'''</div><br/> |
| − | *<math> | + | *<math>Array1</math> is the array of y values. |
| − | *<math> | + | *<math>Array2</math> is the array of x values. |
| + | **RSQ(), returns the square of the Pearson product moment correlation coefficient. | ||
| Line 7: | Line 8: | ||
*This function gives the square of Pearson Product Moment Correlation Coefficient. | *This function gives the square of Pearson Product Moment Correlation Coefficient. | ||
*This function is calculated using the data points of <math>y</math> and <math>x</math> values. | *This function is calculated using the data points of <math>y</math> and <math>x</math> values. | ||
| − | *The formula for PPMC,<math>r</math> is defined by: | + | *The formula for PPMC, <math>r</math> is defined by: |
<math> r= \frac{ \Sigma(x-\bar{x})(y-\bar{y})}{\sqrt {\Sigma(x-\bar{x})^2(y-\bar{y})^2}}</math> | <math> r= \frac{ \Sigma(x-\bar{x})(y-\bar{y})}{\sqrt {\Sigma(x-\bar{x})^2(y-\bar{y})^2}}</math> | ||
where <math> \bar{x}</math> and <math>\bar{y} </math> are Average of the two Samples <math>x </math> and <math>y </math>. | where <math> \bar{x}</math> and <math>\bar{y} </math> are Average of the two Samples <math>x </math> and <math>y </math>. | ||
| − | *This function gives the value of r^2, which is the square of this | + | *This function gives the value of <math> r^2</math>, which is the square of this Correlation Coefficient. |
| − | *The square value can be interpreted as the proportion of the variance in y attributable to the variance in x. | + | *The square value can be interpreted as the proportion of the variance in <math>y</math> attributable to the variance in <math>x</math>. |
| − | *In <math> RSQ( | + | *In <math> RSQ(Array1,Array2)</math>, the value of <math>Array1</math> and <math>Array2</math> must be either numbers or names, array, constants or references that contain numbers. |
| − | *Suppose the array contains text,logicl values or empty cells, like that values are not considered. | + | *Suppose the array contains text, logicl values or empty cells, like that values are not considered. |
| − | *This function will return the result as error when 1. | + | *This function will return the result as error when |
| − | 2. The arguments having only one data point. | + | 1. <math>Array1</math> and <math>Array2</math> are empty or having the different number of data points. |
| − | 3. The arguments that are error values or text that cannot be translated in to numbers. | + | 2. The arguments having only one data point. |
| − | + | 3. The arguments that are error values or text that cannot be translated in to numbers. | |
| − | + | Refer [[Manuals/calci/PEARSON |PEARSON]] for more details. | |
==Examples== | ==Examples== | ||
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|- | |- | ||
! 3 | ! 3 | ||
| − | | 9 || | + | | 9 || 7 || 23 || 11 || 22 || 30 || 6 || 15 |
| + | |- | ||
| + | ! 4 | ||
| + | | 50 || 47 || 26 || 13 || 20 || 14 || 33 || 1 | ||
| + | |- | ||
| + | ! 5 | ||
| + | | 4 || 17 || 25 || 44 || 2 || 9 || -1 || | ||
| + | |- | ||
| + | ! 6 | ||
| + | | 18 || 36 || 40 || 11 || || || || | ||
| + | |} | ||
| + | |||
| + | # =RSQ(A1:A6,B1:B6) = 0.4003286578 | ||
| + | # =RSQ(C1:C6,D1:D6) = 0.02320694105 | ||
| + | # =RSQ(E1:H1,E2:H2) = 0.72060025461 | ||
| + | # =RSQ(E3:E5,G3:G5) = 0.346037364910 | ||
| + | # =RSQ(G3:G5,H3:H4) = NAN | ||
| + | |||
| + | ==Related Videos== | ||
| + | |||
| + | {{#ev:youtube|anebTt-Jbqs|280|center|RSQ}} | ||
| + | |||
| + | ==See Also== | ||
| + | [[Manuals/calci/PEARSON |PEARSON]] | ||
| + | |||
| + | ==References== | ||
| + | [http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient Pearson] | ||
| + | |||
| + | |||
| + | |||
| + | |||
| + | *[[Z_API_Functions | List of Main Z Functions]] | ||
| + | |||
| + | *[[ Z3 | Z3 home ]] | ||
Latest revision as of 16:11, 8 August 2018
RSQ (Array1,Array2)
- is the array of y values.
- is the array of x values.
- RSQ(), returns the square of the Pearson product moment correlation coefficient.
is the array of y values.
is the array of x values.
Description
- This function gives the square of Pearson Product Moment Correlation Coefficient.
- This function is calculated using the data points of and values.
- The formula for PPMC, is defined by:
and 
values.
is defined by:where and are Average of the two Samples and .
where 
and 
are Average of the two Samples - This function gives the value of , which is the square of this Correlation Coefficient.
- The square value can be interpreted as the proportion of the variance in attributable to the variance in .
- In , the value of and must be either numbers or names, array, constants or references that contain numbers.
- Suppose the array contains text, logicl values or empty cells, like that values are not considered.
- This function will return the result as error when
, which is the square of this Correlation Coefficient.
, the value of 1. and are empty or having the different number of data points. 2. The arguments having only one data point. 3. The arguments that are error values or text that cannot be translated in to numbers.
Refer PEARSON for more details.
Examples
| A | B | C | D | E | F | G | H | |
|---|---|---|---|---|---|---|---|---|
| 1 | 12 | 10 | 17 | 21 | 25 | 31 | 19 | 5 |
| 2 | 4 | 37 | 8 | 18 | 0 | 13 | 15 | 41 |
| 3 | 9 | 7 | 23 | 11 | 22 | 30 | 6 | 15 |
| 4 | 50 | 47 | 26 | 13 | 20 | 14 | 33 | 1 |
| 5 | 4 | 17 | 25 | 44 | 2 | 9 | -1 | |
| 6 | 18 | 36 | 40 | 11 |
- =RSQ(A1:A6,B1:B6) = 0.4003286578
- =RSQ(C1:C6,D1:D6) = 0.02320694105
- =RSQ(E1:H1,E2:H2) = 0.72060025461
- =RSQ(E3:E5,G3:G5) = 0.346037364910
- =RSQ(G3:G5,H3:H4) = NAN
Related Videos
See Also
References