mws_gen_reg_bck_regressionintro

# mws_gen_reg_bck_regressionintro - Chapter 06.02...

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06.02.1 Chapter 06.02 Introduction of Regression Analysis After reading this chapter, you should be able to: 1. know what regression analysis is, 2. know the effective use of regression, and 3. enumerate uses and abuses of regression. What is regression analysis? Regression analysis gives information on the relationship between a response (dependent) variable and one or more (predictor) independent variables to the extent that information is contained in the data. The goal of regression analysis is to express the response variable as a function of the predictor variables. The duality of fit and the accuracy of conclusion depend on the data used. Hence non-representative or improperly compiled data result in poor fits and conclusions. Thus, for effective use of regression analysis one must 1. investigate the data collection process, 2. discover any limitations in data collected, and 3. restrict conclusions accordingly. Once a regression analysis relationship is obtained, it can be used to predict values of the response variable, identify variables that most affect the response, or verify hypothesized causal models of the response. The value of each predictor variable can be assessed through statistical tests on the estimated coefficients (multipliers) of the predictor variables. An example of a regression model is the linear regression model which is a linear relationship between response variable, y and the predictor variable, n i x i ..., 2 , 1 , of the form n n x x x y ... 2 2 1 1 0 (1) where n ....... , 1 0 are regression coefficients (unknown model parameters), and is the error due to variability in the observed responses.

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06.02.2 Chapter 06.02 Example 1 In the transformation of raw or uncooked potato to cooked potato, heat is applied for some specific tune. One might postulate that the amount of untransformed portion of the starch ( y ) inside the potato is a linear function of time ( t ) and temperature ( ) of cooking. This is represented as 2 1 0 t y (2) Linear as used in linear regression refers to the form of occurrence of the unknown parameters, 1 and 2 as ,simple linear multipliers of the predictor variable. Thus, the two equations below are also both linear.
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mws_gen_reg_bck_regressionintro - Chapter 06.02...

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