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Correlation Statistics Definition Tutoring

Introduction to correlation statistics definition tutoring:

In mathematics, correlation is one important topic in statistics. Correlation is defined as the relationship between more than one variable. Change in one variable may affecting the other variables also.Correlation is a number which can be used to describe the relationship between two variables. In this article we shall discuss about correlation statistics definition tutoring. Tutoring is used to help thestudents with the step by step solutions for their doubts in online. The following are the formula and examples problems are involved in correlation statistics definition tutoring.


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Correlation statistics definition tutoring - Formula:


Formula for correlation:

Correlation (r) = `[(NsumXY - (sumX) (sumY)) / sqrt ([NsumX^2 - (sumX)^2][NsumY^2 - (sumY)^2])]`

Where
              x and y are the variables.
              b = the slope of the regression line is also called as regression coefficient
              a = intercept point of the regression line which is in the y-axis.
              N = Number of values or elements
              X = First Score
              Y = Second Score
             `sumXY` = Sum of the product of the first and Second Scores
             `sumX` = Sum of First Scores
             `sumY` = Sum of Second Scores
             `sumX^2` = Sum of square First Scores.
             `sumY^2` = Sum of square second Scores


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Correlation statistics definition tutoring - Example problem:


Example 1:

To determine the correlation value for the given set of X and Y values

X Values

Y Values

11

1.7

16

2.3

21

2.9

26

3.5

31

4.1

46

5.3


Solution: 

Let us count the number of values

            N = 6

Determine the values for XY, X2, Y

X Value

Y Value

  X*Y

  X*X

  Y*Y

  11

   1.7

    18.7

   121

   2.89

  16

   2.3

    36.3

   256

   5.29

  21

   2.9

    60.9

   441

   8.41

  26

   3.5

    91.0

   676

 12.25

  31

   4.1

  127.1

   961

 16.81

  46

   5.3

  243.8

  2116

  28.09


Determine the following values `sum X` , `sum Y` , `sum XY` , `sum X^2` , `sum Y^2` .
`sum X` = 151
`sum Y` = 19.8
`sum XY` = 577.8
`sumX^2` = 4571
`sumY^2 ` = 73.74

Correlation (r) = `[(Nsum XY - (sum X) (sum Y)) / sqrt ([NsumX^2 - (sum X)^2][NsumY^2 - (sum Y)^2])]`

                        = `[(6(577.8) - (151) (19.8)) / sqrt ([6(4571) - (151)^2][(6)(73.74) - (19.8)^2])]`

                        = `[(3466.8 - 2989.8)/ sqrt ([27426-22801][442.34-392.04])]`

                        = `[(477)/sqrt ([4625][50.4])]`

                        = `[(477)/sqrt([233100])]`

                        = `[(477)/(482.80)]`

                        = 0.99

                  (r)  = 0.99

Answer:

Correlation (r) = 0.99