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The values listed in table 5 are values for the regression
coefficient, depending on the screw inclination. The
respective calculated standard deviation of the coefficient
is indicated.
A standard deviation that is small in relation to the
coefficient is a sign for a significant influence of the
variable of the coefficient. It can be seen that the standard
deviation for all coefficients lies at a maximum of 3% of the
coefficient value, thus in all reviewed variables one can
assume a significant influence.
To finally assess the quality of the regression
model, the values calculated through the
regression model for the coefficient of velocity
ζ is compared to the determined values ζ*
and graphically presented. Picture 7 shows
the corresponding estimated values ζ over the
determined values ζ* The model is the better,
the closer the points are to the bisecting line.
It can be seen that there a re no major outliers
and the data points of the estimated values of
the coefficient of velocity ζ it the bisecting line.
In terms of numbers the quality of the model can
also be assessed with the help of the radical of
the mean square error.
MQF =
Issue 04 | 2010
1
i
i
∑ k=
1
* 2 ( ζ − ζ )
k
k
(18)
The radical of mean square error in the
current model is √(MQF) = 0,0111. Even in the
smallest determined coefficients of velocity
ζ* this corresponds to an average deviation of
smaller than 3% and proves sufficient accuracy
of the calculated regression model. In order to assess,
where deviations of the model lie, picture 8 shows the
determined and estimated values of the coefficient of
velocity in the various categories. For the sake of limiting
complexity, the screw diameter parameter is not itemized,
since it has the least influence and the diagrams offer very
similar results. It can be seen
that in almost all fields there is a
good concurrence between the
coefficient
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determined data points and the calculated model (curve).
It is only in border areas that there are minor deviations.
Thus the obtained regression model is suitable for
calculation of the coefficient of velocity. The achievable
volume flow I V of an inclined screw conveyor can therefore
simply and reliably be calculated through the equations (6)
and (17).
Pic. 7:
Model fitting for the
coefficient of velocity
β =30° β = 40° β > 40°
Standard
deviation
Table 5:
The regression coefficient of velocity
coefficient
Standard
deviation
coefficient
Standard
deviation
a -0,287003 0,001893 -0,861013 0,005680 -1,146694 0,003376
b -0,795297 0,018035 -0,795313 0,018035 -0,793336 0,008084
c 0,068029 0,000770 0,204090 0,002311 0,272243 0,001381
d 0,023858 0,000757 0,071570 0,002271 0,095512 0,001356
e - - - - -0,000987 0,000016
f 0,958562 0,001882 0,875682 0,005645 0,879204 0,003576
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