Difference between revisions of "Manuals/calci/MCORREL"
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*The above formula is used for simple correlation. | *The above formula is used for simple correlation. | ||
*Now consider the variables x,y and z we define the multiple correlation as: | *Now consider the variables x,y and z we define the multiple correlation as: | ||
| − | <math>R_{zxy}=\sqrt{\frac{r_{xz}^2+r_{yz}^2-2 r_{xz} r_{yz} r_{xy}}{1-r_{xy}^2}</math> | + | <math>R_{zxy}=\sqrt{\frac{r_{xz}^2+r_{yz}^2-2 r_{xz} r_{yz} r_{xy}}{1-r_{xy}^2}}</math> |
*<math>r_{xy}</math> is the correlation of x and y. | *<math>r_{xy}</math> is the correlation of x and y. | ||
*<math>r_{yz}</math> is the correlation of y and z. | *<math>r_{yz}</math> is the correlation of y and z. | ||
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2.<math>Array of Arrays </math>is empty | 2.<math>Array of Arrays </math>is empty | ||
3.The denominator value is zero. | 3.The denominator value is zero. | ||
| − | |||
==Examples== | ==Examples== | ||
Revision as of 17:00, 5 July 2017
MCORREL (ArrayOfArrays)
- 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 ArrayOfArrays} is set of values.
Description
- This function is showing the result for multiple correlation.
- 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 MCORREL (ArrayOfArrays)} ,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 Arrayofarrays} are set of values.
- Correlation is a statistical technique which shows the relation of strongly paired variables.When one variable is related to a number of other variables, the correlation is not simple.
- It is multiple if there is one variable on one side and a set of variables on the other side.
- If we have a series 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 n} measurements 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} 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} written as 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_i} 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_i} 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 i = 1, 2,...n} then the Sample Correlation Coefficient is:
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 CORREL(X,Y)= r_{xy}= \frac{\sum_{i=1}^n (x_i-\bar x)(y_i-\bar y)}{\sqrt{ \sum_{i=1}^n (x_i-\bar x)^2 \sum_{i=1}^n (y_i-\bar y)^2}}}
- 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 means 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} 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} .
- The above formula is used for simple correlation.
- Now consider the variables x,y and z we define the multiple correlation as:
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 means 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}
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}
.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 R_{zxy}=\sqrt{\frac{r_{xz}^2+r_{yz}^2-2 r_{xz} r_{yz} r_{xy}}{1-r_{xy}^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 r_{xy}} is the correlation of x and y.
- 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 r_{yz}} is the correlation of y and z.
- 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 r_{zx}} is the correlation of z and x.
- Here x and y are viewed as the independent variables and z is the dependent variable.
- This function will give the result as error when
1.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 Array of Arrays} are non-numeric or different number of data points. 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 Array of Arrays } is empty 3.The denominator value is zero.