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## 10.9 Formula List

$SSxx=Σx2−1n(Σx)2 SSxy=Σxy−1n(Σx)(Σy) SSyy=Σy2−1n(Σy)2$

Correlation coefficient:

$r=SSxySSxx·SSyy$

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

$y^=β^1x+β^0 where β^1=SSxySSxx and β^0=y-−β^1x-$

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

$SSE=SSyy−β^1SSxy.$

Sample standard deviation of errors:

$sε=SSEn−2$

$100(1−α)%$ confidence interval for $β1$:

$β^1±tα∕2 sεSSxx (df=n−2)$

Standardized test statistic for hypothesis tests concerning $β1$:

$T=β^1−B0sε∕SSxx (df=n−2)$

Coefficient of determination:

$r2=SSyy−SSESSyy=SSxy2SSxxSSyy=β^1SSxySSyy$

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

$y^p±tα∕2 sε 1n+(xp−x-)2SSxx (df=n−2)$

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

$y^p±tα∕2 sε 1+1n+(xp−x-)2SSxx (df=n−2)$