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The study material in the form of ppt. covers the topic of Regression Analysis.

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it changes with a change in independent variable. Dependent variable y is a continuous random variable, whereas the values of the independent variable x are fixed The standard deviation and variance of expected values of the https://testmyspeed.onl/ dependent variable about the regression

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Slide 1 : JSS MAHAVIDYAPEETHA. A DEGREE A HIGHER PURPOSE.

Regression Analysis : Regression Analysis By: Ms. Shilpa Bahl Assistant Professor JSSATE, Noida

Meaning : The statistical method that helps to formulate an algebraic relationship between two or more variables in the form of an equation to estimate the value of a continuous random variable, given the value of another variable is called regression analysis. The variable whose value is estimated is called dependent variable. The variable whose value is used as the basis for the estimate is called independent variable. Meaning

Types : Simple and Multiple Regression models Simple: the relationship between a dependent y and only one independent variable x, then such a regression model is called a simple regression model. Multiple: when more than one independent variable are associated with a dependent variable, then such a regression model is called multiple regression model. Types

Slide 5 : Linear and non linear regression models Linear: if the value of a dependent variable y in a regression model tends to increase in direct proportion to an increase in the values of independent variables, then such a regression model is called a linear model. Non linear: if the line passing through the pair of values of variables x and y is curvilinear, then such a relationship is called non linear.

Assumptions for a simple linear regression model : For every value of the independent variable x, there is an expected value of the dependent variable y and it changes with a change in independent variable. Dependent variable y is a continuous random variable, whereas the values of the independent variable x are fixed The standard deviation and variance of expected values of the dependent variable about the regression line are constant Assumptions for a simple linear regression model

Parameters of Simple Linear Regression Model : The regression equation of y on x y = a + bx (b yx ) is used for estimating the value of y for given values of x. Regression equation of x on y x = c + dy (b xy ) is used for estimating the value of x for given values of y. Parameters of Simple Linear Regression Model

Properties of regression coefficients : The correlation coefficient is the geometric mean of two regression coefficients, i.e. √b xy * b yx If one regression coefficient is greater than one, then other must be less than one. Both of the regression coefficients must have the same sign. The arithmetic mean of regression coefficients b xy and b yx is more than equal to the correlation coefficient r. Properties of regression coefficients

Standard error of estimates : A measure of variation of the observed values of the dependent variable about the least square regression line. The straight line around which the sum of squared residuals is minimum is called least square regression line. Standard error of estimates

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