Regression
Y
X Linear Assumptions
Equivalent Terms 2k Factorials Y = bo +b1X1 +b2X2 ... Pooled Variance s2p Standard Error of Effects sE t statistics: t = E/sE Linear Regression Y = a+bX s2 = SSE/(n-c) Standard Error of Coefficients sa, sb t = b/sb b tsb
Confidence intervals E tsE
^ Y 2s p
^ Y 2 sY^
b^ L
n L X iY
i
L ( L X i) ( L Y i)
2 i
n L X
i
L ( L X i) 2
a^ L ( L Y
L b^ L X i ) / n .
Confusing notation: these n's represent the number of data pairs used to estimate a and b
This n represents the number Standard error of the predicted average of next k Y's at of future n values we xo are predicting Change these to k on page 305 of your book the average of
sY L s ^
( x o L X ) 2 1 L n L( X i L X ) 2 k
Excel Output for Tensile Strength - Brinell Hardness Data
SUMMARY OUTPUT
Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.996642257 0.993295789 0.991061052 4.42703563 5
% Variation in Y =T.S by the relation with X =B.H. (SST-SSE)/SST
s = SSE /( n - c)
n
ANOVA df Regression Residual Total 1 3 4 SS 8711.204067 58.7959334 8770 MS 8711.204 19.59864
SSE SST
Intercept a or b0
Y=a+bX
Coefficients
Standard Error 0.025732839
t 10.01220424 Stat
P-value
Lower 95%
Upper 95%
Intercept X Variable 1
-16.91618802 0.542517535
-1.68956 21.08269
0.189694 0.000233
-48.77952 0.4606241
14.947144 0.624411
Slope b
significance
Confidence interval
X Y 1976 Opponents Team Yds Rush Wins Oakland 1903 Pittsburg 1457 Cinncinati 1917 Denver 1709 Miami 2411 Houston 2072 Seattle 2876
ANOVA df Regression Residual Total 1 5 6
( X i - X ) 2 = 1,320,305
10 10 10 9 6 5 2
Is there a significant relationship Between X = Opponents Yards Rushing and Y = wins? What is R2?
Coefficients Intercept 19.5877364 X Variable 1 -0.0059334
Calculate a Confidence interval for the number of wins for the average of next k = 4 Teams to hold S...