Basic Analysis and Graphing - SAS

126 Performing Bivariate Analysis Chapter 4
Statistical Details for the Bivariate Platform
Pure Error SS
For the Pure Error SS, in general, if there are g groups having multiple rows with the same x value, the
pooled SS, denoted SS p , is written as follows:
SS p
=
where SS i is the sum of squares for the ith group corrected for its mean.
Max RSq
g
SS i
i = 1
Because Pure Error is invariant to the form of the model and is the minimum possible variance, Max RSq is
calculated as follows:
SS( Pure error)
1 –
--------------------------------------------------------------
SS( Total for whole model)
Statistical Details for the Parameter Estimates Report
Std Beta
Std Beta is calculated as follows:
βˆ ( s x
⁄ s y
)
where βˆ
is the estimated parameter, sx and sy are the standard deviations of the X and Y variables.
Design Std Error
Design Std Error is calculated as the standard error of the parameter estimate divided by the RMSE.
Statistical Details for the Smoothing Fit Reports
R-Square is equal to 1-(SSE/C.Total SS), where C.Total SS is available in the Fit Line ANOVA report.
Statistical Details for the Correlation Report
The Pearson correlation coefficient is denoted r, and is computed as follows:
r xy
2
s xy 2 w ------------ where
i
( x i
– x i
)( y i
– y i
)
= s
2 2 xy
= -------------------------------------------------
df
s x sy
Where w i is either the weight of the ith observation if a weight column is specified, or 1 if no weight
column is assigned.