Tisch Environmental TE-5200, Operation Manual

Page: 18 / 34

TE-5200 18 Operations Manual
Using Qstd as our x-axis, and FLOW (corrected) as our y-axis, a slope, intercept,
and correlation coefficient can be determined using the least squares
regression method.
The equations for determining the slope (m) and intercept (b) are as follows:
15. m =
  
 
xy
x y
n
x
x
n
b = y - mx


 



2
2
;
where:
n = number of observations
y =
∑ y/n
x = ∑ x/n
∑ = sum of.
The equation for the coefficient of correlation (r) is as follows:
16.
  
   
r =
xy
x y
n
x
x
n
y
y
n



















 


 

2
2
2
2
where:
n = number of observations
∑ = sum of
Before these can be determined, some preliminary algebra is necessary.
∑ x,
∑ y, ∑ x
2
, ∑ xy, ( ∑ x)
2
, ( ∑ y)
2
, n, y, and x need to be determined.
17.

x = 1.632 + 1.529 + 1.483 + 1.435 + 1.316 = 7.395
18.

y = 2.34 + 2.21 + 2.15 + 2.07 + 1.94 = 10.71
19.

x
2
= (1.632)
2
+ (1.529)
2
+ (1.483)
2
+ (1.435)
2
+ (1.316)
2
= 10.991635