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# How to learn Correlation and Regression for JEE Main 2015

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How to learn Correlation and Regression for JEE Main 2015 by ednexa.com

How to learn Correlation and Regression for JEE Main 2015 by ednexa.com

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• 1. Correlation and Regression Introduction “If it is proved true that in a large number of instances two variables tend always to fluctuate in the same or in opposite directions, we consider that the fact is established and that a relationship exists. This relationship is called correlation.” (1) Univariate distribution : These are the distributions in which there is only one variable such as the heights of the students of a class. (2) Bivariate distribution : Distribution involving two discrete variable is called a bivariate distribution. For example, the heights and the weights of the students of a class in a school. (3) Bivariate frequency distribution : Let x and y be two variables. Suppose x takes the values x1, x2, …. xn and y takes the values y1, y2 , …, yn, then we record our observations in the form of ordered pairs (x1, y1), where 1 ≤ I ≤ n, 1 ≤ j ≤ n. If a certain pair occurs fij times, we say that its frequency is fij. The function which assigns the frequencies fij’s to the pairs (xi, yj) is known as a bivariate frequency distribution. Covariance Let (x1, xi); 1 = 1, 2, …,n be a bivariate distribution, where x1, x2, …. xn are the values of variable x and y1, y2 , …, yn, those of y. Then the covariance Cov (x, y) between x and y is given by
• 2. n n i i i i i 1 i 1 1 1 Cov(x,y) (x x)(y y) or Cov(x,y) (x y x y) n n        where, n i i 1 1 x x n    and n i i 1 1 y y n    are means of variables x and y respectively. Covariance is not affected by the change of origin, but it is affected by the change of scale. Correlation The relationship between two variables such that a change in one variable results in a positive or negative change in the other variable is known as correlation. (1) Types of correlation (i) Perfect correlation : If the two variables vary in such a manner that their ratio is always constant, then the correlation is said to be perfect. (ii) Positive or direct correlation : If an increase or decrease in one variable corresponds to an increase or decrease in the other, the correlation is said to be positive. (iii) Negative or indirect correlation : If an increase or decrease in one variable corresponds to a decrease or increase in the other, the correlation is said to be negative.
• 3. (2) Karl Pearson's coefficient of correlation : The correlation coefficient r(x, y), between two variable x and y is given by, x y n n n i i i i i 1 i 1 i 1 2 2n n n n 2 2 i i i i i 1 i 1 i 1 i 1 2 2 Cov(x,y) Cov(x,y) r(x,y) or , Var(x) Var(y) n x y x y r(x,y) n x x n y y (x x)(y y) d r (x x) (y y)                                                                      2 2 xdy . dx dy  (3) Modified formula :     2 2 2 2 dx. dy dxdy nr dx dy dx dy n n                               , where dx x x;dy y y    Also xy x y Cov(x,y) Cov(x,y) r var(x).var(y)     .
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