03a_SLR - Statistical Techniques II EXST7015 Simple Linear...

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Statistical Techniques II EXST7015 Simple Linear Regression 03a_SLR 1
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The objective 0123456789 1 0 X - the independent variable 20 25 30 35 Y - the dependent variable Given points plotted on two coordinates, Y and X, find the best line to fit the data. 03a_SLR 2
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The concept Data consists of paired observations with a presumed potential for the existence of some underlying relationship We wish to determine the nature of, and quantify, the relationship if it exists. Note that we cannot prove that the relationship exists by using regression (e.g. we cannot prove cause and effect). Regression can only show if a "correlation" exists, and provide an equation for the relationship. 03a_SLR 3
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The concept (continued) Given a data set consisting of paired, quantitative variables, and recognizing that there is variation in the data set, we will define, POPULATION MODEL (SLR) Y ij = β 0 + β 1 X i + ε i This is the line we will fit. 03a_SLR 4
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The concept (continued) We must estimate the population equation for a straight line The Population Parameters estimated are µ y.x = the true population mean of Y at each value of X β 0 = the true value of the Y intercept β 1 = the true value of the slope, the change in Y per unit of X µ y.x = β 0 + β 1 X i 03a_SLR 5
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Terminology Dependent variable - variable to be predicted Y = dependent variable (all variation occurs in Y) Independent variable - predictor or regressor variable X = independent variable (X is measured without error) 03a_SLR 6
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Terminology (continued) Intercept - value of Y when X = 0, point where the regression line passes through the Y axis NOTE: units are "Y" units Slope - the value of the change in Y for each unit increase in X NOTE: units are "Y" units per "X" unit 03a_SLR 7
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Terminology (continued) Deviation - distance from an observed point to the regression line, also called a residual. Least squares regression line - the line that minimizes the squared distances from the line to the individual observations. 03a_SLR 8
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Regression line 0123456789 1 0 X - the independent variable 20 25 30 35 Y - the dependent variable Deviations 03a_SLR 9
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Regression calculations All calculations for simple linear regression start with the same values. These are, Σ X i , Σ X i 2 , Σ Y i , Σ Y i 2 , Σ X i Y i , n Calculations for simple linear regression are first adjusted for the mean. These are called "corrected values". They are corrected for the MEAN by subtracting a "correction factor".
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This note was uploaded on 12/29/2011 for the course EXST 7087 taught by Professor Wang,j during the Fall '08 term at LSU.

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03a_SLR - Statistical Techniques II EXST7015 Simple Linear...

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