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10.9 Formula List

SSxx=Σx21n(Σx)2  SSxy=Σxy1n(Σx)(Σy)  SSyy=Σy21n(Σy)2

Correlation coefficient:

r=SSxySSxx·SSyy

Least squares regression equation (equation of the least squares regression line):

y^=β^1x+β^0 whereβ^1=SSxySSxx andβ^0=y-β^1x-

Sum of the squared errors for the least squares regression line:

SSE=SSyyβ^1SSxy.

Sample standard deviation of errors:

sε=SSEn2

100(1α)% confidence interval for β1:

β^1±tα2sεSSxx(df=n2)

Standardized test statistic for hypothesis tests concerning β1:

T=β^1B0sεSSxx(df=n2)

Coefficient of determination:

r2=SSyySSESSyy=SSxy2SSxxSSyy=β^1SSxySSyy

100(1α)% confidence interval for the mean value of y at x=xp:

y^p±tα2sε1n+(xpx-)2SSxx(df=n2)

100(1α)% prediction interval for an individual new value of y at x=xp:

y^p±tα2sε1+1n+(xpx-)2SSxx(df=n2)