Presentation on regression analysis
- 2. MEANING OF REGRESSION The dictionary meaning of the word Regression is ‘Stepping back’ or ‘Going back’. Regression is the measures of the average relationship between two or more variables in terms of the original units of the data. And it is also attempts to establish the nature of the relationship between variables that is to study the functional relationship between the variables and thereby provide a mechanism for prediction, or forecasting.
- 3. IMPORTANCE OF REGRESSION It provides estimate of values of dependent variables from values of independent variables. It can be extended to 2 or more variables, which is known as multiple regression. It shows the nature of relationship between two or more variable Regression analysis helps in three important ways:-
- 4. METHODS OF STUDYING REGRESSION REGRESSION GRAPHICALLY ALGEBRAICALLY DEVIATION METHOD FROM ASSUMED MEAN DEVIATION METHOD FROM A.M LEAST SQUARES LEAST SQUARES FREE HAND CURVE OR
- 5. ALGEBRAICALLY METHOD 1. Least Square Method The regression equation of x on y is: x=a+by where, X=Dependent variable Y=Independent variable The regression equation of y on x is : Where, Y=Dependent variable X=Independent variable And the values of a and b in the above equations are found by the method of least of Squares-reference . The values of a and b are found with the help of normal equations given below: 1 ∑x= na+b∑y ∑xy=a∑y+b∑𝑦2 2 ∑r=na+b∑x ∑xy=a∑x+b∑𝑥2
- 6. The calculation by the least squares method are quit cumbersome when the values of X and Y are large. So the work can be simplified by using this method. The formula for the calculation of Regression Equations by this method: regression equation of x on y- (x-x )=B 𝑥𝑦 ( y- y ) regression equation of y on x- (y- y )=Byx (x-x ) where, Bxy and Byx = regression coefficient 2. Deviation from the arithmetic mean method: Bxy =∑xy and Bxy = ∑xy ∑ y2 ∑x2
- 7. DEVIATION FROM ASSUMED MEAN METHOD When actual mean of x and y variables are in functions, the calculations can be simplified by taking the deviations from the assumed vale The regression equation of x on y- ( x - x ) = Bxy ( y - y ) The regression equation of y on x- ( y - y ) = Bxy ( x - x ) But, here the values of Bxy and Byx will be calculated by following formula: Bxy = N ∑ dxdy - ∑dx∑dy Byx = N ∑dxdy - ∑dx∑dy N ∑ d2y -∑d2y N ∑ d2x - ∑d2x 3. Deviation from assumed mean value
- 9. THANK YOU 1. SUJEET SINGH 2. ISHWOR KHANAL 3.BISHAL KATHIWADA 4. MANOJ BASNET 5. RABIN SHRESTHA PRESENTED BY