report on coeff of correlation

8/17/2019 Report on Coeff of Correlation

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B.DEVI PRAVALLIKA

8701,MTECH-CIVIL

REPORT ON COEFFICIENT OF CORRELATION

(COMPUTATION MATHS)

The function between two variables are related to one another

and the pattern of the data points on the scatter plot can

illustrate various patterns and relationships, including

• data correlation

• positive or direct relationships between variables

• negative or inverse relationships between variables

• non-linear patterns

As we conned our attention to the analysis of observations on a

single variable. There are many phenomenon where one variable

are related to the changes in the other variable.

For example the yield of a crop varies with the amount of the

rainfall, the price of a commoditiy increases with the

reduction in its supply. From the above examples we have

notied that change in one variable is associated with the

change in other variable this relation which exists is known

as CORRELATION. uch data connecting two variables is

known as !"ivariate population#

DEFINITION OF CORRELATION

The change in one variable depends on the change in

another variable is known as correlation. it is denoted by !r#

and it is mentioned as -$ % r % $ the value should lie

between these limiting position. in case of solving the


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problems the straight line tting is used y= ! "# and the

normal e&uations are derived using this straight line

e&uation'

( y ) na * b +x( xy) a+x * b+x

correlation than a study using social science data. The quantity r , called the linear

correlation coefficient , measures the strength and the direction of a linear

relationship between two variables. The linear correlation coefficient is sometimes

referred to as the Pearson product moment correlation coefficient in honor of its

developer Karl Pearson. The value of r is such that -1 r !1. The ! and " signs

are used for positive linear correlations and negative linear correlations,

respectively.

Positive correlation: #f x and y have a strong positive linear correlation, r is

close to !1. $n r value of e%actly !1 indicates a perfect positive fit. Positive

values indicate a relationship between x and y variables such that as values

for x increases the value y increases

Negative correlation: #f x and y have a strong negative linear correlation, r is

close to -1. $n r value of e%actly -1 indicates a perfect negative fit. Negative

values indicate a relationship between x and y such that as values for x increase,values y decrease.

No correlation: #f there is no linear correlation or a wea& linear correlation, r is

close to '. A value near zero means that there is a random, nonlinear

relationship between the two variables. (ote that r

is a dimension less quantity)

that is, it does not depend on the units that are being employed.


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$ perfect correlation of * 1 occurs only when the data points all lie e%actly on a

straight line. #f r + !1, the slope of this line is positive. #f r + -1, the slope of

this line is negative. $ correlation greater than '. is generally described as strong ,

whereas a correlation less than '. is generally described as weak . These value can

vary based upon the type of data that is being e%amined.

f an increase or decrease in the values of one variable

corresponds to an increase or decrease in the other ,the

correlation is said to be positive. f the increase or decrease

in one corresponds to the decrease or increase in the other

the correlation is said to be negative. f there is no

relationship indicated between the variables they are said to

be independent or uncorrelated. To obtain a measure of relationship between two variables we plot their

corresponding values on the graph taking one of variables on

the x axis and the other along y axis. /et the origin is shifted

to x and y where x and y are the new corrdinates. 0ow the

points x and y are so distributed along over the four

&uardants of xy plane that the product is positive in the rst

and third &uardants but negative in second and fourth

&uardants. The algebric sum of the products can be taken as

describing the trend of dots in all the &uardants

f ( xy is positive , the trend of dots is through the rst and

the third &uardants

f ( xy is negative , the trend of dots is through the second

and fourth &uardants

f the ( xy is 1ero, the points indicate no trend that is points

are evenly distributed through the four &uardants

Method of Calculation:

a2 3irect method substituting the value of 4x and 4y in the

above formule we get r)+56789+5+62 .


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Another form of the formula 9$2 which is &uite handy for

calculation is

r) n+xy-+x+y 7 8: 9n+x-9+x2 ; x :n+y-

9+y2;; This formula is used when the means are integers

b2 tep deviation method'the direct method becomes very large ,lengthy and tedious if

the means of two series are not integers in such cases ,use

is made of assumed means if dx and dy are step deviations

from the assumed means

r) n+ dxdy- +dx +dy78: 9n +dx-9+dx2; x :n+dy-9+dy22;

where dx)9x-a27h dy)9y-b27k


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measures and describes the strength and direction of the

relationship"ivariate techni&ues re&uires two variable scores from the

same individuals 9dependent and independent variables2.

?ultivariate when more than two independent variables 9e.ge@ect of advertising and prices on sales2. ariables must be

ratio or interval scaleC&%%+ &' &%*+&t also called as Bearson product moment correlation

coe=cient. The algebraic method of measuring the

correlation is called the coe=cient of correlation.T/%% % *y +/%% &%%+$ &' &%*+&

Carl BearsonDs


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E#*%3 Eelationship between yield with both rainfall and

fertili1er together is multiple correlations

P+* C&%*+&

The correlation is partial if we study the relationship between twovariables keeping all other variables constant. E#*%3 The

Eelationship between yield and rainfall at a constant temperature

is partial correlation.

P&%+%$ &' +/% C&%%+ &' &%*+&


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report on coeff of correlation

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