J. Hon. Sci. 
Vol. 1 (1): 68-70, 2006 

Statistical modelling for pre-harvest forecast: an illustration with rose 

K. S. Shamasundaran and R. Yenugopalan 
Section of Economics and Statistics 

Indian Institute of Horticultural Research 
Hessaraghatta Lake Post, Bangalore-560 089, India 

E-mail: sham@iihr.emet.in 

ABSTRACT 

Crop yield forecast plays a vital role in arriving at pre-harvest yield estimate of a standing crop and to identify 
the stage at which reliable forecasting could be made before final harvest. In this paper, an attempt has been 
made to apply the regression technique for prediction of yield in rose. Rose, is an important flower crop not only 
for internal market but is also intended for export, and since it shrivels, estimation of yield of a standing crop 
before its actual harvest is essential. Based on results a model was developed, which showed that information 
from the first two pickings of a standing crop could be used to forecast rose yield to an extent of 77% two months 
before final harvest. It is also suggested to have a minimum sample size of 20 % to develop such a forecast model. 

Key words: Goodness of fit statistics, statistical modelling, yield forecast 

INTRODUCTION 

Commercial cultivation of roses has gained 
importance in recent years in India due to a growing demand 
for these flowers in both domestic and export markets. India, 
blessed with diverse agro-climatic conditions, has an 
immense potential to increase the productivity and, in turn, 
yields maximum return, in overseas market for this crop. 
This can be achieved by developing a suitable model to 
predict the actual yield of a standing crop and subsequently 
identify the stage within which forecasting could be made 
to the desired extent. To this end, it is imperative to develop 
a model through which growers and policy makers could 
frame suitable management strategies for maximizing crop 
productivity and net return. In this regard, statistical 
modelling plays a vital role in developing appropriate 
forecast models, on a strong scientific footing, for crop yield 
prediction. Shamasundaran and Singh (2003) made a 
beginning in this direction. 

In the present study, an attempt has been made to 
develop multiple regression models for obtaining a pre-
harvest estimate of yield of rose based on information 
pertaining to several pickings. Goodness of fit of the models 
developed was carried out by statistically testing the 
computed regression coefficients and working out measures 
model adequacy. 

MATERIAL AND METHODS 

An investigation was carried out at the Indian 

Institute of Horticultural Research, Bangalore during 1994-
95 for yield prediction in rose cv. Happiness. Two hundred 
and fifty six samples were used in this study. All the 
recommended cultural practices with a spacing of 75 cm x 
75 cm were followed uniformly for the entire plot. Data on 
yield in terms of number of flowers/plant from several 
pickings were recorded and consolidated. The first picking 
was made eleven months after planting. Subsequent 
pickings were made at an interval of 45 days. 

Linear correlation coefficient among harvests done 
during several pickings and total yield were computed and 
statistically tested. Further, multiple regression models were 
developed by regressing harvest pertaining to different 
pickings with the cumulative yield by utilizing the principle 
of least squares (Lewis-Beck, 1993). The following 
measures of goodness of fit statistics were used to judge 
the adequacy of the model developed (Agostid'no and 
Stephens, 1986): 

Mean squared error (MSE) 
A 

M S E = [ E ( Y t - Y t ) ^ / n ] 

Coefficient of Determination (R )̂ 

R^= l - [ 2 : ( Y t - Y ) 2 / [ 2 : ( Y t - Y t ) ^ ] 

where Ŷ  represents the harvest/yield at time t. However, 
while fitting regression models to the data considered, it 

mailto:sham@iihr.emet.in


Shamasundaran and Venugopalan 

may be noted that even an addition of one more independent 
variable to the model would result in increase in R̂  value 
(Kvelsth, 1985). Hence, to test the significance of the added 
variable, regression coefficients were subjected to t-test 
statistic analysis (Lewis-Beck, 1993). 

RESULTS AND DISCUSSION 

Linear [simple(r) and multiple(R)] correlation among 
yield (total) and individual pickings yield were computed 
are presented in Tables 1 and 2. Results revealed that there 
existed a highly significant relationship in almost all the 
pickings at 1 % level, either individually or in combination 
with total yield. Further, it was noticed that the first picking 
gave rise to R̂  of 70% followed by others and the least was 
noticed with the fifth picking. When multiple correlation 
and regression was carried out, it revealed that all the 

pickings, individually or in combination, had significantly 
higher association with total yield ranging from 0.3889 to 
0.9060. It was found that more than 80% of R̂  noticed with 
all the pickings together followed by first three and first 
four pickings. The first two pickings and the same along 
with four pickings; the first five pickings except second 
gave rise to an R̂  of more than 77% yield prediction. 
Further, as discussed earlier, inclusion of additional 
information about the harvest obtained in every pickings, 
R̂  value tends to increase further. To this end, regression 
coefficients derived by including an additional variable were 
tested for its statistical significance. Results presented in 
table 3 indicate that inclusion of X^ variable into the model 
yielded non-significant regression coefficient, as indicated 
by t-statistic value of 1.04, which falls outside the 
acceptance region. Similarly, it may be further observed 

Table 1. Results of correlation (r) among individual pickings and total yield 

DV IV r 
6 ) 0.84** 

2 0.51** 
3 0.53** 
4 0.39** 
5 0.15 

** Significant at 1% 

a 
2.5487 

-0.0172 
-0.4903 
0.0992 
0.4205 

DV- Dependent Variable IV-lndependent Variable 
1-First picking (X,) 2-Second picking (X^) 
4-Fourth picking (X )̂ 5- Fifth picking (X5) 

b, 
0.3682 
-
-
-
-

b, 

0.0759 
-
-
-

3-Third picking (X,) 
6.Total yield (X,) 

Table 2. Results of multiple correlation (R) among pickings and total yield 

DV IV R 
6 1,2 0.88** 

1,3 0.72** 
1,4 0.81** 
1,5 0.79** 
2,3 0.72** 
2,4 0.75** 
2,5 0.57** 
3,4 0.74** 
3,5 0.51** 
4,5 0.39** 
1,2,3 0.89** 
1,2,4 0.88** 
1,2,5 0.84** 
2,3,4 0.81** 
2,3,5 0.73** 
3,4,5 0.74** 

1,2,3,4 0.91** 
1,2,3,5 0.90** 
1,3,4,5 0.89** 
2,3,4,5, 0.85** 
1,2,3,4,5 0.91** 

a 
-1.6575 
3.4425 
3.2340 
1.6152 
6.2107 
7.0901 
7.9559 
5.8523 
8.5244 
9.7716 

-1.1389 
2.7167 
1.2488 
4.5190 
5.9351 
5.8802 

-0.8506 
0.6815 
1.1059 
4.3604 

-0.8571 

b , 
1.7039 
1.2992 
1.2362 
1.4667 
-
-

-
-
-
1.4853 
1.0018 
1.2886 
-
-
-
1.2582 
1.1200 
1.1847 
-
1.2599 

b, 
1.9354 
-
-
-
3.3277 
1.3168 
1.2598 
-
-
-
2.0963 
0.9228 
0.7775 
2.4385 
1.3418 
-
1.8455 
0.8992 

3.4531 
1.8408 

b, 

-
0.2385 
-
-

b, 

0.8668 

-
1.1362 

-
1.4238 
1.3072 
-
0.3648 
-
-
1.3419 
1.4194 
-
0.5842 
1.0148 
0.8509 
1.3611 
0.5831 

b. 
-
-
-
0.1139 
-

b. 

-
1.0299 
-
-
1.5209 
-
1.8123 

1.2908 
-
1.1600 
-
1.3873 

-
0.6845 
-
0.8678 
1.5174 
0.6835 

b, 

-
-
-
0.0387 

b, 

-
-
1.2010 
-
-
1.0325 
-
1.0150 
0.1404 
-

1.2007 
-
1.0604 
-
-
1.1987 
0.9536 
1.0970 
0.0043 

RM%) 
69.83 
25.96 
27.80 
15.12 
2.20 

R̂  (%) 
77.43 
60.09 
65.85 
62.56 
52.37 
58.90 
32.11 
54.60 
25.68 
15.25 
79.30 
77.92 
71.28 
66.33 
53.97 
54.64 
82.08 
81.78 
79.58 
71.72 
82.08 

** Significant at 1"; 
DV- Dependent Variable 
1-First picking (Xj) 
4-Fourth picking (X^) 

IV-lndependent Variable 
2-Second picking (X )̂ 
5- Fifth picking (X,) 

3-Third picking (X )̂ 
6.Total yield (X )̂ 

/ Hon Sci. 
Vol. 1(1): 68-70, 2006 

69 



Statistical modelling for pre-harvest forecast 

Table 3. Results of goodness of fit statistics along with the selected models 

IV R2 MSE Model and (t-statistic) Significant IV 
,2 

,2,3 

,2,3,4 

,2,3,4,5 

0.88 

0.89 

0.82 

0.82 

6.05 

6.01 

5.69 

6.52 

Y = -1.66+1.7X,+1.93Xj 
(5.44) (2.09) 

Y = -1.14+1.48X,+2.09X2+0.36X3 
(3.95) (2.24) 

Y = -0.85+1.26X,+1.84X2+0.58X3+0.68X, 
(3.1) (1.98) (1.54) (1.3) 

Y = -0.85+1.26X,+1.8X2+0.58X3+0.68X,+0.004X5 
(1.1) (0.005) 

X,,X, 

X,,X, 

X „ X , 

X, 

Figures in parentheses indicate t-statistic values 
DV- Dependent Variable IV-Independent Variable 
1-First picking (X,) 2-Second picking (X^) 
4-Fourth picking (X^) 5- Fifth picking (X5)\ 

3-Third picking (Xj) 
6.Total yield (X^) 

that inclusion of an additional variable into the model results 
in non-significant regression estimates. Thus, results 
indicate that information from two pickings could predict 
the yield to an extent of 77 %. Further, corresponding 
regression coefficients were significant as indicated by the 
t-statistic values, which fall inside the acceptance region 
of 1.96. Moreover, the mean square error in reduction also 
strengthens our conclusion for identifying a model based 
on the first two pickings. Hence, the model developed 
showed that information from the first two pickings of a 
standing crop could be used to forecast rose yield 
considerably two months before final harvest. It may also 
be stressed here that as reported by Shamasundaran et al 
(2003), a minimum sample size of 20% of the population 
is required to get a good estimate to develop such a forecast 
model. 

ACKNOWLEDGEMENT 

The authors are grateful to Director, Indian Institute of 

Horticultural Research, Bangalore for providing all 
facilities to conduct this investigation. 

REFERENCES 

Agostid'no, R.B. and Stephens M.A.1986. Goodness of 
Fit Techniques. Marcel Dekker, New York 576p 

Lewis-Beck, S. M.1993. Regression Analysis. Sage Publ., 
New York. 433p 

Kvelseth,T.O 1985. Cautionary note about R .̂ The Amer. 
Stat., 39:279-85. 

Shamasundaran, K. S. and.Singh, K. R 2003. Yield 
forecasting in tuberose (Polyanthes tuberosa Linn.) 
as effected by association of various characters. J. 
Om. Hort., 6:372-75. 

Shamasundaran, K. S. Venugopalan, R and Singh, K. R 
2003. Optimum sample size for yield estimation in 
certain commercial crops. J. Orn. Hart., 
6:2AA-A1 

(MS Received 16 February, 2006 Revised 6 June, 2006) 

J. Hort. Sci. 
Vol. 1(1): 68-70, 2006 

70