10.9 Formula List

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

Correlation coefficient:

r=SSxy√SSxx·SSyy

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

ˆy=ˆβ1x+ˆβ0  where ˆβ1=SSxySSxx  and ˆβ0=ˉy−ˆβ1ˉx

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

SSE=SSyy−ˆβ1SSxy.

Sample standard deviation of errors:

sε=√SSEn−2

100(1−α)% confidence interval for β1:

ˆβ1±tα∕2 sε√SSxx (df=n−2)

Standardized test statistic for hypothesis tests concerning β1:

T=ˆβ1−B0sε∕√SSxx (df=n−2)

Coefficient of determination:

r2=SSyy−SSESSyy=SS2xySSxxSSyy=ˆβ1SSxySSyy

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

ˆyp±tα∕2 sε √1n+(xp−ˉx)2SSxx (df=n−2)

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

ˆyp±tα∕2 sε √1+1n+(xp−ˉx)2SSxx (df=n−2)