Solution we shall represent production of paddy by y

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Solution We shall represent production of paddy by Y and the rainfall by X. Therefore, the estimated regression line is given by Y a bX where a Y bX and Y X r b
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167 From the given details, we obtain 9.05 0.82 0.512 14.5 b and 56.5 0.512(102.5) 4.02 a The estimated regression line is given by 4.02 0.512 Y X Therefore, the estimated production of paddy when the rainfall is 120 cm is given by 4.02 0.512(120) 65.46 Y Thus, the estimated paddy production is 65.46 quintals/acre. 18.3.2.2. Lines of Regression A line of regression is the line which gives the best estimate of one variable X for any given value of the other variable Y. Line of Regression X on Y It is the line which gives the best estimate for the values of X for a specified value of Y. It is given by X Y XY X X r Y Y X X b Y Y Where X , Y are means of X series and Y series respectively, X , Y are S.D of X and Y series respectively and r is the correlation coefficient between X and Y and XY b is the regression coefficient of X on Y. . ., X XY Y i e b r It can also be put in the form X a bY Where an intercept of the line and b is the slop of the line X on Y. Line of Regression Y on X It is the line which gives the best estimate for the values of Y for a specified value of X. Regression equation of Y on X is given by Y X YX Y Y r X X Y Y b X X YX b is the regression coefficient of X on Y.
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168 . ., Y YX X i e b r It can also put in the form Y a bX Where a is the intercept of the line and b is the slope of the line Y on X. 18.3.2.3. Properties of Regression Coefficients 1) The correlation coefficient is the geometric mean of two regression coefficients. i.e., yx xy r b b 2) If one regression coefficient is greater than one, then other regression coefficient must be less than one. 3) Both regression coefficients must have the same sign. 4) The correlation coefficients will have the same sign as there of the two regression coefficients. 5) Regression coefficients are independent of origin but not of scale. 6) The arithmetic mean of regression coefficients is more than or equal to the correlation coefficient. Example - 3 The following data relates in the production and supply of 10 company in Tamil Nadu. Obtain the two equations of the regression lines. Also estimate the expected production whose supply is 60 and the expected supply whose production is 200. Production 172 179 122 198 186 144 180 164 222 219 Supply 55 56 38 64 59 48 56 53 69 68 Solution Regression equation Y on X is Y X YX Y Y r X X Y Y b X X Regression equation X on Y is X Y XY X X r Y Y X X b Y Y Where X X N Y Y N
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169 2 2 2 2 YX XY N XY X Y b N X X N XY X Y b N Y Y     X Y 2 X 2 Y XY 172 179 122 198 186
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