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# LCT21 - Introduction to Business Statistics Lecture 21...

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1 Introduction to Business Statistics Lecture 21 Regression Analysis I Terminology: z Y dependent variable , the variable to be modelled or predicted z X independent variables , predictors, regressors A model is a theoretical description that tries to explain a phenomenon. What requires of a model is that it z should be simple. z can capture the important aspects of the phenomenon. z needs to fit the data well.

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2 The Model Equation for Simple Linear Regression: } , part random part systematic 1 0 ε β β + + = 43 42 1 X Y where ε has a normal distribution with mean 0 and variance 2 σ whatever values X take. Thus, x x X E x x X X E x X Y E 1 0 1 0 1 0 ) | ( ) | ( ) | ( β β ε β β ε β β + = = + + = = + + = = . z The systematic part is the conditional mean!! z Note that ε = ) | ( X Y E Y , that is, the Y value minus the conditional mean equals the random part. Remark : From now on, we will use E ( Y | X ) to denote the conditional expectation for simplicity. .
3 The Population Regression Line X X Y E 1 0 ) | ( β β + = is very useful in explaining and summarizing Y using X . Three interpretations of the simple linear regression model z Imperfect relationship interpretation: The model equation without the random part describes a perfect linear relationship. The presence of the random part makes the relationship imperfect.

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LCT21 - Introduction to Business Statistics Lecture 21...

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