Regression

regression , equation, multiple regression

1. Regression

2. Regression The earliest form of regression is the method of least squares. Regression means – return to origin It is a measure of the average relationship between two or more variables in terms of the original units of data.

3. In other term Regression is the theory of estimation of unknown value of a variable with help of a known value of another variable. The relationship between two variables say X and Y may be linear straight line or non linear. The regression line is also called the estimating line.

4. Y= a + bx The regression of y on x where y treated as dependent variable and x as an independent variable. The regression of x on y where x treated as dependent variable and y as an independent variable . B will be the slope of the line.

5. Y = a + b x

6. If one of the two regression coefficient is more than unity and the other must be less than unity. i.e b yx > 1 then b xy must < 1 If the regression coefficient are positive then the pearson’s correlation coefficient r is also positive and vice versa.

7. The pearson’s correlation coefficient r is the geometric mean of the two regression coefficient.

8. Regression analysis is a collective name for techniques for analysis of numerical data consisting of values of dependent variable and one or more other variable known as the independent variables.

9. In linear regression, only two variables are considered and the function is linear The equation that can be written as y= a + bx Y is the variable to be estimated also called dependent or response variable. X is the variable explaining the variation also called the independent or predictor variable. b is the slope of the line. a is the y intercept of the line [ value of y when x=0 ]

10. Y = a + b x

11. Method of least square If line is drawn so that the squared deviations of the observed points from that line are minimised . The procedure is called method of least square.

12. The expected value of one variable corresponding to the observed value of the other variables is read directly from the scatter diagram.

13. Multiple regression It has three or more variables It is often used in social and behavioural science to determine the personality variables and social indicators which predict social adjustment. It is used in testing hypothesis

14. L i near regression model is used in forecasting trends in prevalence of diseases, in forecasting survival rates of persons exposed to disease or risk factor. Non linear regression model are used for forecasting seasonal trends in diseases, child birth or availability of employment. Beta analysis a measure of risk used by share market experts is a type of regression analysis.

15. Precaution The regression line should not be unduly extended beyond the range of actual observation. For instance data pertaining to children should not be extrapolated to adults.