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).
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
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.
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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