28SLR

# 28SLR - Statistical Techniques I EXST7005 Simple Linear...

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Statistical Techniques I EXST7005 Simple Linear Regression

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Simple Linear Regression Measuring & describing a relationship between two variables Simple Linear Regression allows a measure of the rate of change of one variable relative to another variable. Variables will always be paired, one termed an independent variable (often referred to as the X variable) and a dependent variable (termed a Y variable). There is a change in the value of variable Y as the value of variable X changes.
Simple Linear Regression (continued) For each value of X there is a population of values for the variable Y (normally distributed). Y

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Simple Linear Regression (continued) The linear model which discribes this relationsh is given as Yi = b0 + b1Xi this is the equation for a straight line where; b0 is the value of the intercept (the value of Y when X = 0) b1 is the amount of change in Y for each unit change in X. (i.e. if X changes by 1 unit, Y change by b1 units). b1 is also called the slope or REGRESSION COEFFICIENT
Simple Linear Regression (continued) Population Parameters 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 1Xi this is the population equation for a straight line

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Simple Linear Regression (continued) The sample equation for the line describes a perfect line with no variation. In practice there i always variation about the line. We include an additional term to represent this variation. μ y.x = β 0 + β 1Xi + ε i for a population Yi = b0 + b1Xi + ei for a sample when we put this term in the model, we are describing individual points as their position on the line, plus or minus some deviation
Simple Linear Regression (continued) Y

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the SS of deviations from the line will form the
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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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28SLR - Statistical Techniques I EXST7005 Simple Linear...

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