Simple Linear Regression. The term linear regression implies that  Y|x is linearly related to x by the population regression equation  Y|x =  +  x.

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Presentation transcript:

Simple Linear Regression

The term linear regression implies that  Y|x is linearly related to x by the population regression equation  Y|x =  +  x where the regression coefficients  and  are parameters to be estimated from the sample data. Denoting their estimates by a and b, respectively, we can then estimate  Y|x by  y from the sample regression or the fitted regression line  y = a + bx where the estimates a and b represent the  y intercept and slope, respectively. The symbol  y is used here to distinguish between the estimated or predicted value given by the sample regression line and an actual observed experimental value y for some value of x.

Estimating the Regression Coefficient. Given the sample {(x i, y i ); i = 1, 2, …, n}, the least squares estimates a and b of the regression coefficients  and  are computed from the formulas and

x y