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Systems management class lectures_144661413-nsuClass-lecture-doc

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Chapter 12 (Simple Regression) (a) The sample correlation coefficient (measures the strength of linear relationship)|: s ∑ ( x − x )( y − y ) / n r = xy = ∑ ( x − x )( y − y ) 2 2 = sx s y ( x − x ) ( y − y ) ∑ ∑ ∑ ( x − x )∑ ( y − y ) n n (Population) Regression equation: y = β 0 + β1 x + ε i (See 12.4, Page-411) Estimated regression equation: yˆ = b0 + b1 x where, the regression coefficient: b1 = sxy sx = ∑ ( x − x )( y − y ) , and ∑ (x − x ) 2 b) Test of correlation coefficient, H 0 : ρ = 0 , Test statistics: t = c) Test of regression coefficient: H 0 : β1 = 0 , Test statistics: t = where, se(b1 ) = se ∑ ( xi − x )2 , se = ∑(y − y) intercept, b0 = y − b1 x . r n−2 (1 − r 2 ) : t (n − 2) b1 se(b1 ) 2 i d)12.4 The Explanatory Power of a Linear Regression Equation (see page-418) SSE 2 2 2 The coefficient of determination: R = 1 − , SST = ∑ ( yi − y ) , SSE = ∑ ( yˆi − y ) SST SST=SSR+SSE, (See page-421) 2 e) If r is significant then, | r |> . n 12.21 (pp417, modified) A corporation administers an aptitude test to all new sales representatives. Management is interested in the extent to which this t ...
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