M. G. B A R N E S , W. R. A K E S O N a n d N. P E N C E1
Received for publication April 10, 1974
Introduction
Accurate prediction of w7eight and sugar losses of stored sugar- beets at the beginning of the storage period is useful because it enables the total losses to be estimated by the end of harvest, and it helps to explain the causes of such losses.
Regression analysis has been used previously in agricultural pre- diction; for example, to predict the yield of corn (4)2 and of crested wheatgrass (2), and to analyze relationships between yield and weather- in sugarbeets (1). However, no reference was found for the use of this method to predict actual storage losses.
Methods and Materials
Calculations were made using the Burroughs ASSIST statistical- program package (3). T h e weather data is from CLIMATOLIGICAL DATA (5), and all other data is from records of T h e Great Western Sugar Company. Data from 1 969 were eliminated because they are not comparable to other years' data due to frozen beets.
Multiple linear regression analysis was used to find those inde- pendent variables which best explain the historical losses. These fac- tors were considered for use as independent variables:
1. Campaign length.
2. Average number of storage days.
3. Deviation from normal temperatures for weekly periods in October.
4. Weekly maximum and minimum temperatures in October.
5. Percent of beets delivered during weekly periods in October.
6. Percent of beets delivered by October 8, 16, or 27.
7. Precipitation during the period September 15 to October 3 1 . 8. Percent of beets piled after first occurrence of 24°F. or below, and also 20°F. or below.
9. Deviation from normal of average monthly temperatures in November and December.
'Data Analyst, Sr. Plant Physiologist, and Operation Research Analyst, respectively, The Great Western Sugar Company, Agricultural Research Center, Longmont, Colorado 80501.
2Numbers in parentheses refer to literature cited.
V O L . 18, No. 2, O C T O B E R 1974 1 8 3
Each geographical region was analyzed separately with the same technique. Detailed results are given for one region, ,North Central Colorado, which includes the Eaton, Greeley, Loveland, Longmont, and Brighton factory districts. Weather data for this region are from the Greeley and Longmont 2ESE stations.
Factors were eliminated if their correlation with the shrink was of magnitude less than 0.3, or because two factors showed correlation of magnitude 0.3 or more with each other and could not be used in the same equation.
Factors of the first type were eliminated initially. If no more than about eight factors remained, equations were generated by using each variable with as many of the other variables as possible, in all combina- tions which did not include inter-correlated variables in the same equation. If more than eight factors remained, those which showed the highest correlation with the shrink were used to generate equations first and other variables added or substituted if necessary. Sometimes, statistical tests showed undesirable characteristics in these equations.
In these cases, either one or more variables were dropped from the equations, or the whole set of variables was discarded.
After the elimination of variables had been completed, the equa- tions were compared and the one with highest multiple R-square became the predictor equation. This method was used to find a weight shrink and a sugar loss equation for each region.
Results and Discussion
In North Central Colorado, the weight shrink equation variables are:
(1) Campaign length.
(2) Percent of beets delivered by October 16.
(3) Maximum temperature, October—Week 4.
T h e sugar loss equation uses these variables:
(1) Campaign length.
(2) Percent of beets delivered by October 16.
(3) Maximum temperature, October—Week 2.
(4) Maximum temperature, October—Week 4.
T h e most variables in any equation is four, the least is two. More factors actually affect storage losses, but these effects are over- shadowed by r a n d o m variability under field conditions, so only the strongest factors are useful in prediction. All of the equations for sugar loss use only three basic factors: campaign length, October tempera- tures (November temperatures for Ohio), and rate of delivery.
T h e values estimated from the equations for North Central Col- orado are compared (Table 1) with actual values for the period 1960-1971. As in all regions, the sugar loss equation gives better results
JOURNAL. or THE A. S. S. B. T.
T a b l e 1 . — C o m p a r i s o n o f e s t i m a t e d w i t h t r u e v a l u e s o f s h r i n k n o r t h c e n t r a l C o l o r a d o .
Y e a r
1971 1970 19G8 1967 1966 1965 1964 1963 1962 1961 1960
Actual 1 2 9 . 1 3 *
9 7 . 5 1 7 3 . 5 9 8 8 . 5 9 8 7 . 5 7 5 9 . 8 0 108.25 1 16.36
9 3 . 8 6 114.74 130.55
S u g a r L o s s
E s t i m a t e 128.52*
100.95 75.61 9 3 . 8 6 8 1.49 5 9 . 8 0 105.21 1 13.93 100.34 107.24 133.18
Actual 2 1 0 . 5 3 +
9 1 . 1 9 78.69 48.46 2 8 . 6 6 2.61 162.58 167.80 1 1 8.29
8 5 . 4 6 105.78
W e i g h t L o s s
Estimate' 1 78.22+
7 6 . 6 0 71.91 6 2 . 5 3 2 3 . 4 5 - 0 . 5 2 144.87 177.18 1 5 0 . 0 8 1 12.04 103.18
—
- P e r c e n t of 1 1-vear not I h c e n t r a l C o l o , a d o s u g a r loss m e a n . t P e r c e n t of 1 I-year n o r t h c e n t r a l C o l o r a d o w e i g h t loss m e a n .
than the weight shrink equation, due mainly to variability in the method of measuring weight shrink.
A comparison of the multiple R-square and the standard error of estimate for the equations (Table 2) indicates their accuracy; the weight shrink equations account for between 74 and 91 percent of the varia- tion in weight shrink, and the sugar loss equations atxouiit for 89 to 96 percent of the variation in sugar loss. Company-wide comparisons of predicted shrink values with the actual values are in Table 3.
T a b l e 2 . — C o r r e l a t i o n c o e f f i c i e n t s a n d s t a n d a r d e r r o r o f e s t i m a t e s o f m u l t i p l e r e g r e s s i o n e q u a t i o n s .
M u l t i p l e R - S q u a r e S t a n d a r d E r r o r o f E s t i m a t e R e g i o n W e i g h t l o s s Sugar Loss W e i g h t L o s s Sugar L o s s
\ . C . C o l o r a d o N o r t h e a s t C o l o r a d o N e b r a s k a W y o m i n g M o n t a n a N o r t h e r n O h i o
* P e r c e n i o f 9-year c o m p a n y - w i d e weight loss m e a n . T P e r c e n t o f 9-year c o m p a n y - w i d e s u g a r loss m e a n .
T h e final test of the usefulness of the equations is how' storage losses predicted in advance compare with the actual losses (Table 4).
T h e first projection was made by November 5, 1972 (December 5 for Ohio) using an estimate of campaign length, and the second was made later using the actual campaign length. T h e accuracy of these predic- tions shows the great value of this technique.
Summary
A study was carried out to determine factors to use in multiple linear regression equations for predicting weight and sugar shrink in
0.91 0.74 0.91 0.83 0.79 0.81
0 . 9 6 0.89 0.94 0 . 9 5 0.91 0.89
1 8 . 8 3 * 2 2 . 6 8 20.1 1 3 7 . 6 6 3 2 . 1 0 3 5 . 9 5
5.44+
7.19 8.17 1 1.08 19.25 2 1.97