Topic_10.0___Linear_Regression_and_Correlation

Topic_10.0___Linear_Regression_and_Correlation - Simple...

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Simple Linear Regression and Correlation Ash Genaidy
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Introduction This topic introduce methods for analyzing relationships between pairs of quantitative variables. In this regard, three inter-related issues should be considered Whether an association exists between two variables by testing the hypothesis of statistical independence; The study of the strength of such an association (i.e.,correlation); The form of the relationship (to estimate a formula predicting the response variable from the knowledge of the explanatory variable).
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Introduction The analyses conducted in these three aspects of the relationship between two quantitative variables are collectively called regression analysis.
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Topic Outline Linear relationships (form of relation) Least Squares Prediction Equation Linear Regression Method – taking into account the variability of data about the straight line Pearson correlation for describing the strength of linear relationship Statistical Inference for regression analysis
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Linear Relationship Notation for response and explanatory variables Let Y denote the response variable and X the explanatory variable Linear Function The formula Y= α + β X expresses the response variable Y as a linear function of the explanatory variable X The formula maps out a straight-line graph with slope β and Y- intercept α .
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Linear Relationships At X=0, Y= α . The slope β equals the change in Y for a one- unit change in X. If β is positive, then Y increase as X increases. If β is negative, then Y decreases as X increases. When β =0, the graph of a linear function is a horizontal line.
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Least Squares Prediction Equation Using sample data, one can estimate the linear model relating Y and X. The process treats α and β in the linear function Y= α + β X as unknown parameters and yields estimates of these parameters. The estimated linear function then provides prediction about Y at fixed values for X.
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Least Squares Prediction Equation The method of least squares provides the prediction equation having the minimal value of sum of squared errors (SSE), that is, The least square estimates a and b are the values determining the equation for which the sum of squared error SSE is a minimum. Note: the difference between observed and predicted
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Topic_10.0___Linear_Regression_and_Correlation - Simple...

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