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ANALYSIS cgHAWAIIGREENHOUSE TOMATO DATA

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gricu~turalep<;>rtmgNice

Hawaii Department of AgrrcultureUS. Department of Agriculture

ANALYSIS OF HAWAII GREENHOUSE

TOMATO DATA

Prepared By:

Fred B. Warren, Senior Math StatisticianUnited States Department of AgricultureStatistical Reporting Service, U. S. D. A.

Statistical Research DivisionYield Research Branch

for

Hawaii Agricultural Reporting ServiceA cooperative function of

HawaiiDepartment of AgricultureMarketing & Consumer Services Division

United StatesDepartment of Agriculture

Statistical Reporting Service

ANAL YSIS Of i1l1.1 '1<1I GREENHOUSE TOMATO DATA. By Fred B. Wa rren,Statistical Research Division, Economics and Statistics Service,U. S. Department of Agriculture, June 1981.

ABSTRACTOne hundred seventeen weeks of temperature and greenhouse

tomato condition data were evaluated to identify factors whichmight be related to weekly sales and fruit set. Prototype moaelswere developed from the given data both to determine the types ofvariables which would be most useful and to determine thepossible gains in precision which might be obtained. Theprincipal findings of this evaluation are that: data of the typeevaluated can be used to develop reasonable forecast andestimation mod~ls for numbers of fruit set, for the amount ofsaleable fruit, and for the average weight per fruit, and thatthe numbers of fruit set and average weight of fruit at maturityresponded differently to different levels of maximum and minimumtemperatures at different stages of development.

Key words:temperature.

Yield modeling, linear regression, tomatoes,

************************************************************** This paper was prepared for limited distribution to the ** research community outside the U. S. Department of Agri- ** culture. The views expressed herein are not necessarily ** those of ESS or USDA. **************************************************************

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TABLE OF CONTENTS

ANALYSIS OF HAWAII GREENHOUSE TOMATO DATAINTRODUCTION .ANALYSIS

Initial AnalysisWeekly Plots of Fruit Set and SalesDaily Condition and Temperature Data:

Number of Fruit Set: .Sales .\.,r e i gh t per Fr u i t

APPENDIXDATA

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111223

58

1 1

1515

ANALYSIS OF HAWAII GREENHOUSE TOMATO DATA

INTRODUCTION

The data Gsed in this analysis was compiled by a commercialgreenhouse tomato grower in Hawaii. It was then passed to th8Hawaii State Statistical Office (ESS-Statistics) for analysis,particularly to define those factors which related specificallyto production. This task, and the data, was then referred to theYield Research Branch, Statistical Research Division.

Difficulties with the data included the following: (1)Estimates of the number of fruit set and of sales were recordedby weeks for the entire operation, even though the actual areo inproduction varied widely over the 117 week period; (2) Estimatesof the numbers of fruit set were obtained by counts on'representative' plants, rather than a random sample of pla~ts;(3) Temperatures generally were recorded only on weekdays; and(4) while the reported conditions were computed by some formulawhich included the effects of sunlight, wind, temperatur~ andhumidity, the actual weights used were not recorded.

ANALYSIS

The analysis was directed both towards determinir.g Ulepossibility of using the observed temperature and "conditlGn"data to predict the components of production, i.e., the number offruit set and the average weight per fruit at harvest, andtowards direct predictions of the pounds of saleable fruit.(1)

--------------------------------.---------- - - ---_.(1) "Condition" was reported daily, on a scale of 1 to 1C.Factors considered in determining daily condition values were (1)the amount and duration of sunlight, (2) the presence andduration of wind, and (3) temperature "duration" and humidity.These factors were not given specific weights.

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Assumptions required by this analysis are that:1. The "representative plant" procedure used for obtaiLltJ[,

the numbers of fruit set did produce estimates of the actualnumbers which, if not unbiased, at least had a constant (13Sthroughout the entire period.

2. The number of fruit sold as a proportion of fruit setW;l~i c.;on:;Ltn1. thr'oughout U1e enti re period.

3 . The i.lnlO unt 0 f timer e4uire d for the f ru it tom d t ure wasconstant throughout the entire period.-

4. All plantir.gs were of the same size and stayeo inproduction for the same amount of time.

5. The reported condition figures were basea upon .omeunchanging objective criteria.

6. The reported temperatures were uniform for ~llgreenhouses in the complex.

Because the reported numbers of fruit set are estl~atesde riv ed fro m co untson "repre sentat ive" pIa nts , any cor re le:, t 1.cnor regression analyses involving the number of fruit set wil~ notbe as good as if the actual counts, even for small units, coulohave been compared with saleable produce from the same units.

Initial ~~The initial analysis of the data was limited to:

(a) Plotting weekly totals of fruit set, and of thepounds of fruit sold, over time.

(b) Correlating daily reports of condition, an~ ofmaximum and minimum temperatures over time.

Weekly Plot~~uit S~_~d SalesBecause the actual number of plantings in production at any

time was not given, plots of the weekly fruit set and sales catawere used to determine the period of time during which the n~mberof plantings, as indicated by the data for fruit set and sales,would be comparatively stable. As shown in Figure 1, there WaS arapid increase in the number of fruit set each week from week 1until about week 24. This resulted from a rapid increasE intotal plantings during this period. Then, aside fromirregularities in fruit set and sales which may be related to theweather, the number of plantings in production appeared to besomewhat constant from week 25 through 109. However the numberof fruit set was not reported after week 109. Also, sales durjL[,weeks 110-117 were considerably below the period just prececing.These events were taken to indicate that there was a drasticreduction in the number of plantings in production during WEeks110-117. Therefore, the analysis to relate the observed vJluesof condition and of temperature to the number of fruit set waslimited to the data for weeks 25 through 109. Also, since there

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Iappears to be about an 8 to 10 week lag between fruit :Jet. andsales, the analysis to relate condition and temperature d2ta to~ctual sales was limited to weeks 34 through 109.

PLOT OF FRUIT.wEEK 5'''801. useD IS F .....•..PWT OF SAlESOWHK S'''801. USED 15 5-

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Figure 1:wef:'ks.

Numbers of frui t set and pounds of tomatoes sol (, I l'J

Daily maximum and minimum temperatures were grouped by ~~ccorrelated with condition codes. This was to determine how wellthey were related (See Table 1). Both daily and weekly averagedata were also plotted and regressed over time to determine ifthere appeared to be any long term factors in the data. (Theeffects of any seasonal cycles in the data would appear to beminimal, since the first and last 14 weeks of the study periodoverlap the months of November through February.)

The principal findings from this stage of the analysis ~Ierethe highly significant downward trends over time for (1) reporteddaily conditions, (2) daily ranges in temperatures, and (3)reported maximum daily temperatures. There was also a very highpositive correlation between the daily reports of condition a~dthe maximum daily temperatures. That is, high daily maximumtemperatures tended to be associated with high condition values.

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Table 1: Coefficients of correlation (r) between reported Gullycondition codes, daily maximum and minimum temperatures and tln;e,and probabilities (p) that the computed values of r ~il c' liot::;ignificantly different from zero, Hawaii Greenhouse TomCit. ,-i,d",11-7-76 to 2-3-79. (n=569)

TemperatureVaricble Time Condition Maximum

Time r 1 •000 -0.296 -0.112 0.156 -c. 17 4p(r=O) 0.000 <0.001 0.007 <0.001 <-G.OOl

Condition r -0.296 1 •000 0.638 -0.249 C.638p(r=O) <0.001 0.000 <0.001 <0.001 <0.;:)01

Maximum r -0 .112 0.638 1 •000 -0.092 C.038temperature p(r=O) 0.007 <0.001 0.000 0.028 <0.001

~:ini!llum r 0.156 -0.249 -0.092 1 .000 -c .cu:1temperature p(r=O) <0.001 <0.001 0.028 0.000 <0.001

Although still highly significant, the correlation bet'vleel! criereported daily conditions and the minimum daily temperatures WaSsmaller than for condition versus maximum temperature. Also thecorrelation of condition with minimum temperatures was negativerather than positive. This implies that low minimum temperaturestended to result in high condition values. The negativecorrelation between minimum temperatures, and both the maximumand daily range of temperature may be associated with periods ofclear skies. Clear skies would be associated with a gredterdegree of nighttime cooling and more sunlight during theday--hence higher maximum temperatures and higher daily conditionvalues.

Normalized weekly average condition and temperature valueswere plotted over weeks. These plots (Figures 2a and 2b)indicate that (1) there was no significant seasonal pattern inthe fluctuations of the daily maximum temperatures, 2) the weeklyaverage condition values did follow the pattern establishec bythe weekly average high temperatures, but (3) that there was asignificant seasonal pattern in the daily minimum temperatures.Means, standard deviations, and maximum and minimum values of thereported daily values are in Table 2.

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Table 2:maximumnumbersweights2-3-79.

Simple statistics for daily reports ofand of minimum temperatures, and for

of fruit set, of total sales, and ofper fruit, Hawaii greenhouse tomato

condition arJo ofweekly val ue~> ofderived ave-raged a t a, 1 1 - 7 -( l' to

-----------------------------------------------------------_._-~--Variables

Mean StandardError

C. V. Mi nimum ~'ic..l/~H;t.;[;,(% )-------------------.-------------------------------------------~--

Condition 5.277 2.07 25.9 v-'

Temperature:*High 29.44 3.52 11 .9 16 41Low 12.95 2.45 19.0 4 1SRange 16.49 4.48 27.3 4 31

Fruit set per week, (000)weeks 24 to 101 176.9 15.67 8.9 146.58 L:C: ,; .54

Sales per week, (000)weeks 34-109 47.81 9.77 20.4 29.18 69.31

Average weight perfruit sold**weeks 34-109 0.271 0.056 20.6 0.163 ().392

-----------------------------------------------------------------* Degrees Celsius** Weight per fruit computed as pounds sold that week divided bythe average number of fruit set 8 and 9 weeks earlier.

This portion of the analysis was limited to the data lromweeks 25 through 109. This was because the first 24 weeksapparently represent a period of buildup in production, and til~rewere no observations for numbers of fruit set during the last 8weeks. Factors considered in attempting to model the number offruit set each week were the average and extreme temperaturesrand the condition values both for that week and for the previousweek.

The first portion of this analysis was to determine if thesame trends observed over the entire period for reported dallycondition and temperatures also held for the abbreviated subsetof weekly averages. After adjusting the regression coefficientsfor differences in the numbers of observations, the data in Table3 indicates that there were essentially no differences betweenthe two sets of trends.

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Figure 2A: Normalized weekly average conditions and maximumtemperatures, by weeks.UCJlD I

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Figure 2B: Normalized average reported conditions and minimumtemperatures, by weeks.

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I1

ITable 3: Coefficients of correlation (r), probabilities ofnonsignificance (p), and regression coefficients for dailycondition and temperature observations over time for 117 weeksvs. weekly averages for only weeks 25 through 109, HawaiiGreenhouse Tomato data, 11-7-76 to 2-3-79.

Type of ObservationVariables Daily

(117 weeks)Weekly Averages(weeks 25-109)

Observations 569 85Condition r -0.296 -0.471

P <0.001 <0.001b -0.003 -0.025

Maximum r -0.112 -0.131temperature p 0.007 0.235

b -0.0016 -0.0090Minimum r 0.156 0.153

temperature p <0.001 0.161b 0.0016 0.015

Given that there were no differences in the trends foreither condition or for weather, the next step in the analysiswas to use a stepwise 'max r-sq' regression procedure to identifythe variables which would be most useful in modeling the numberof fruit to be set in any particular week. Variables evaluatedin this analysis included both the linear and quadratic effectsof maximum, minimum and average high and low daily temperaturesand condition reports for both the current and for the precedingweek as well as the number of fruit set the previOUS week. Forthe range of temperature values observed, the best model (best interms of having the smallest residual mean square error) for thispurpose would contain the variables listed in Table 4. Thismodel has a coefficient of correlation (r) of 0.64 and thestandard deviation of the residuals is 12,538. Given the overallweekly average number of fruit set of 175,838, this implies thatabout two out of every three predictions from this model wouldhave been within 7.2 percent of the actual number. With respectto the overall mean, this model would have a relative precisionof about 0.65.(2)

(2) The relative precision of one model with respect to another

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Table 4: Variables for estimating weekly numbers of fruit set,with regression coefficients and F-values, Hawaii greenhousetomato data, weeks 25 through 109.-----------------------------------------------------------------

Variable b------------------------------------------------------------------144909.3

340.111503.231275.30

2.256- 0.000005

InterceptAverage condition last week

--squaredHighest minimum daily temperature

(Celsius) observed this weekHighest maximum daily temperature

(Celsius) observed this weekNumber of fruit set last week

-- linear-- squared

10.457.632.851.851.34-----------------------------------------------------------------

The functional relationships represented by this group ofvariables could be defined as follows. First, there is a verystrong positive and non-linear relationship between growingconditions the previous week and the number of fruit set duringthe current week. Second, and within the range of temperaturevalues observed, there is a strong positive and linearrelationship between high minimum temperatures and the number offruit set during a particular week. Also, the regressionprocedure rejected weekly average minimum temperatures in favorof the highest daily minimum temperature. High maximum dailytemperatures are also desirable but not as much as high dailyminimum temperatures. Finally, there is an overall positivenon-linear relationship between the number of fruit set duringthe previous week and the number of fruit set during the currentweek.

SalesThe second stage of the analysis was to cumulate weekly

averages of indicated conditions and of maximum and mlnlmumtemperatures. These were lagged over both weekly and three weekintervals. The lagged three-week cumulations were also squared.Therefore, the augmented set of observations for a particularweek included the sales for that week, the linear effects of theweekly temperature and condition values, and both the linear andquadratic effects of the cumulated three-week values. The

is expressed as the ratio of the variances of the errors of thetwo models. In this case, the variance of the differencesbetween the reported numbers of tomatoes set and the numberestimated by the model would be divided by the variance of theweekly deviations from the overall mean.

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augmented (lata set also included the averiJge weekly llumtJcl ,;1frui t set 8, 9, and 10 weeks prev iously. In order to el jnu ~l<..:ll'the variability which resulted from both the initial startup andthe tail off in production during the final 8 weeks, thisanalysis was limited to the sales from weeks 34 through 109.

Principal findings from this phase of the analysis ir.c~~de:1. The variables most highly correlated with the s2Jes

during a particular week were the average high temperature aurl~6the tenth week before harvest (r= 0.444), the average condit.l~-,ll4to 6 weeks before harvest (r= -0.384), the range of average d~ilytemperatures during the tenth week before harvest (r= 0.382), theweek itself (r= 0.378), and the square of the average condit~onduring the fourth to sixth weeks before harvest (r= -0.377).~3)With 76 observations, all of these correlations are statistic~llydifferent from zero at the .001 level of probability. Howcve~the coefficient of correlation for the linear component of cheaverage condition 4 to 6 weeks before harvest is only slibhtlylarger than the coefficient for the quadratic component. 1t;15indicates that the quadratic component really is not imporc2nt.

2. Although the individual correlations are hi~hlysignificant, statistically, individually they are not lGrgeenough to support a forecast model. Therefore the analysis viastaken into a stepwise "Max-R-sq" multiple regression to sort outthe variables which would interact to form the most efficientmodel. (The best model is defined here as being the one forwhich the sum of squares of the differences from the regres~i0nsurface is least.)

The best multiple regression (Table 5) had a R-sq of G.73and a standard deviation of the differences between actual andpredicted weekly sales of about 5,540 pounds. This computes ~~ arelative standard error (CV) of about 11.6 percent. Thi~) elTlTis only about one-half as large as the 20.4 percent CV com~utedfor the weekly deviations of weekly sales from their own mean.The relative precision of the model with respect to the overdllmean was 0.32.

An apparent weakness of this model lies in the smallcontribution to the estimated sales which comes from the numberof fruit set. This may only indicate that the tomato plant tendsto compensate for small fruit sets with larger tomatoes.

(3) The rationale for the negative correlation between weeklysales and the average 'condition' 4 to 6 weeks earlier could bethat, since there was a high positive correlation between thedaily condition reports and the maximum daily temperatures, thenegative correlation would indicate that tomatoes at that SlJbeof maturity develop better with relatively lower temperature~.

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Table 5: Variables for estimating weekly sales of tomatoe~, w~t,Lregression coefficients and F-tests of their significance, fl<H-:al.itomato greenhouse data, weeks 34 through 109.----------------------------------------------------------~---,. _.-Variable b---------------------------------------------------------------~-~InterceptNumber of fruit set eight weeks

before harvestSum of average weekly conditions for _

7 to 9 weeks before harvestSum of weekly average maximum

temperatures for -1 to 3 weeks before harvest4 to 6 weeks before harvest7 to 9 weeks before harvest

-1878077.224

0.0589

-1653.529

1910.637-1285.69941103.464

~.26

• 1 .2

c ~, . '\ 1lc.221 "~ • 7 9

Squares of sums ofweekly average conditions for -

1 to 3 weeks before harvest4 to 6 weeks before harvest

weekly high average temperatures for-7 to 9 weeks before harvest

weekly low average temperature for1 to 3 weeks before harvest7 to 9 weeks before harvest

Weekly average high temperature for theeighth week before harvesttenth week before harvest

Weekly average low temperature for thetenth week before harvest

-41.388 • L,433.300 .97

-220.625 1 b. 69

9. 129 21 .9C-12.641 L:::' ~;3

1033.110 ( .651323.894 ~~ • f) S

839.901 I • (()----------------------------------------------------------~-,-----It should be noted that the most important variables in •..Le

multiple regression equation, as defined by the "F"-values, arenot the same variables which had the highest linear correlati~ll.Also, one variable could be said to appear three times in thatthe weekly average high temperature for the eighth week is alsoincluded in the linear and quadratic effects for the su~ ofaverage maximum temperatures of weeks 7 to 9 before harvest.

The model coefficients (b's) listed in Table 5 indicateL.llatmaximum production would result from the following combinati0n cffactors.

1. A maximum number of fruit were set. Within the range oftemperatures reported, both maximum and minimum temperatur_~

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during the eighth and tenth weeks before harvest shoula be Li8h.2. For the first three week period (7 to 9 weeks before

har'vest), maximum daily temperatures should be high but tlllnirrd.;j[il

daily temperatures and the observed conditions should be low.3. For the second three week period (4 to 6 weeks before

harvest), the daily maximum temperatures should be low but. tIleobserved conditions should be high.

4. For the final three week period (1 to 3 weeks beIGreharvest), daily maximum and minimum temperatures again shoulc behigh and the observed conditions should be low.(4)

Because the above model requires condition and temper2t.uredata up to the week of harvest, it can be used only to estiffiateproduction for the current week. However, marketing specialisLs,etc., could reasonably want to predict production in advance ofactual harvest. Therefore a similar analysis which excluded ~lldata not available within three weeks of harvest was conducted.This was both to illustrate what might be done and to point cutthe loss of precision which should be expected when using ~ lessthan full season model. The variables and regres~ioncoefficients for such a model are listed in Table 6. Asexpected, the R-sq for this model is smaller (0.61 vs. 0.73) andthe standard deviation of the errors is larger (6510 vs. 5541).However, it may be of sufficient accuracy for some purposes.

Wei g h t-.Qe..L-IL.1lit

Since no actual weights per fruit sold were included with thedata, weekly average weights per fruit sold were computed fromthe reported weekly sales for weeks 11 through 117 and from thereported numbers of fruit set 8, 9, and 10 weeks earlier.Factors considered in attempting to model the average weight offruit at harvest included the lagged three-week cumulatior:~ ofcondition and of temperature plus the reported numbers of fr~itset 8, 9, and 10 weeks before harvest.

A stepwise 'max r-sq' regression analysis of the above Uatashowed that the highest correlations were obtained when thedependent variable was weekly sales divided by the reporteanumber of fruit set 8 weeks earlier. The best model (again, bestfrom the standpoint of having the smallest residual mean square)used thirteen variables and resulted in a R-sq of 0.77. Thestandard deviation of the residuals was 0.031 pounds. Variablesand regression coefficients for the 'best' model are listed inTable 7.

--------- ---------------------- ------ --- --. - ---(4) Considering the overall high positive correlation betvleenmaximum daily temperatures and condition, the indication thattemperatures should be high but that condition should be lowhints at some type of complex interaction.

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Table 6: Variables for predicting weekly sales of tomatoes tnreeweeks before harvest, with regression coefficients and F val~es,Hawaii tomato greenhouse data, weeks 34 through 109.------------------------------------------------------------.-.----Variable b

---------------------------------------------------------------InterceptNumber of fruit set eight weeks

before harvestWeekly average high temperature for the

tenth week before harvestWeekly average low temperature for the

eighth week before harvestSum of average weekly conditions for

7 to 9 weeks before harvest

-2050694.760

-0.0639

2071.507

-3268.936

-7691.265

1 .32

1::;.5,

26.07

Ic.:;8

Sum of weekly average maximum temperaturesfor 7 to 9 weeks before harvest

Sum of weekly average minimum temperaturesfor 4 to 6 weeks before harvest

Squares of sums ofweekly average conditions for

7 to 9 weeks before harvestweekly high average temperatures for

7 to 9 weeks before harvestweekly low average temperature for

4 to 6 weeks before harvest

44751.807

4365.578

168.865-240.503

-48.768 0.02-----------------------------------------------------------_._----The mod e1 co efficien ts (b' s) lis tedin Tab 1e 7 w0u1d i ["~1y

that the largest (heav iest) tomatoes would resul t fror;.thEfollowing combination of factors.

1. The number of fruit set 8 weeks earlier is relativelysmall. In fact, the fewer fruit set, the larger they will be.

2. Within the range of temperatures reported, ~ightemperatures, both minimum and maximum, from 8 to 10 weeks beforeharvest are desirable.(5)3. For the first 3 weeks after fruit set (7 to 9 weeksbefore harvest), high daytime temperatures and low nightLimetemperatures are desirable. The response to higher daytim~

(5) Interestingly, the data presented in Table 5 indicates thathigher temperatures during this period are conducive to largernumbers of fruit being set. This would appear to be at varicc.l1cewith 1.

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-----------------------------------------------------~------_ .. ---

1 1 .35

14.6S

16.50

29.0312.7:,18.17

b

-0.005900

-0.00000099

0.011880-0.007391

0.222322

-10.47702Number of fruit set eight weeks

earlier

Intercept

Sum of weekly average lowtemperatures for -

7 to 9 weeks before harvest

Sum of weekly average hightemperatures for -

1 to 3 weeks before harvest4 to 6 weeks before harvest7 to 9 weeks before harvest

Sum of average weekly conditions for -7 to 9 weeks before harvest

-------------------.---------------------------------.------.----.

Table 7: Variables for predicting average weight of ton,C:.iL,ue::.;(pounds per fruit) at harvest, with regression coefficients :indF-tests of their significance, Hawaii tomato greenhouse oata,weeks 34 through 109.

It

III

1

II

0.000053

-0.0002360.000189

Squares of -sums of weekly

1 to 3 weeks4 to 6 weeks

sums of weekly7 to 9 weeks

sums of weekly1 to 3 weeks

average conditions forbefore harvestbefore harvestaverage high temperaturesbefore harvest -0.001192average low temperaturesbefore harvest

9.855.05

17 . 13

22.441

Weekly average high temperatures -8 weeks before harvest10 weeks before harvest

0.0058220.008181

2.6~[..29

Weekly average low temperatures -10 weeks before harvest 0.006056 2.42

week period (4 to 6 weeks eel (,reare low daytime temperatures:":Ld

temperaturesincrease.

4. For the second threeharvest), desirable factorshigh condition values.(6)

is non-linear, tapering off as

------- ---- --------------- --------- _.-- ---- -- -.- ---(6) Considering the high positive correlation between re~ortedcondition figures and the daily maximum temperatures (Table 3),this particular combination appears odd.

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5 . For the fin aI th ree vJ eek per i0 d (1 to 3 wee k s (;e I u n::harvest), desirable factors are a combination of high maxind ..•t.i ondminimum temperatures with low condition values.

\~h i let h e ab0 ve ana1y sis did inc1udeb 0 th the 1i ne :Jt' , ! LiquadrCltic effects of the observed and derived vari8blE's, then:was no attempt to examine the possible "threshold" effE:;ct:oofextreme daily and/or weekly temperature values. (7) (Thel.:;,tadoes not suggest that any "threshold" temperatures wereobserved.)

The varic:bles listed in Table 7 are virtually the samE: "rJeCc.which appear in Table 5. Also the relative importance, asmeasured by the computed "F" statistics, of the seven hignestranking variables in each model is identical. Therefure,considering that the the multiple R-sq's of the two models arevery close (0.77 for weight per fruit vs. 0.73 for total sal~s),there would seem to be little advantage in computing prGb2SiEsales as the product of separate estimates of the number of lr~itset and the average weight per fruit.

----- ----~----- --.---------- - - --_._- -- ------ ----------- - -(7) "Threshold is defined here as beingplant's response to its environmentexample, the temperature may become tooblooms to develop.

a level at whichbecomes asymptotic.

high or too low fornil

l:"orany

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III APPENDIX

DATA

The data set obtained fronl the Hawaii State Stc:tisticalOffice contained the following information for 117 consecutiveweeks of greenhouse operation.

1. Month, day and year for the FRIDAY of the calendar ~eekin which the observations were taken. The dates given ranf;e J.~r'o:"11-7-76 to 2-3-79.

2. The total number of fruit set that week.(8)3. The number of pounds of tomatoes sold that week.4. Daily(9) observations of maximum and minimum ternperat~res

plus appraisals (on a scale of 1 to 10) of growingconditions(10)

in the greenhouses. Daily observations were recorded Handaythrough Saturday.

Plantings reportedly were made at two week intervals. i~ ISnot known how long a particular planting stayed in production orhow many plantings were made. The data also did not indicate ifall the plantings were the same size.

The basic data, as received from the Hawaii State StatisticalOffice, is resident on the USDA Washington Computer Center (ViCC)a san 0S f i1e , DSN=RAD 14 •TOM ATO. DATA . The rei s a1so 8 t !d' ecmember SAS dataset (edited) on WCC, DSN=RAD1~.SASD.TOMATO.DATA.The member names are "TOMATO", "FRUIT" and "LAGS". "TOfvlATO"contains the basic data but with the following editingchanges:(11)

--- -------.--- ~- ---_._---~---- ----------- ----_ .._--- -(8) '~umbers of fruit set' were extrapolated from count~ of'pea-size' fruit on ten 'representative' plants Hl ;:3chgreenhouse.(9) No observations were taken on Sunday, any time the week of12-23-77, most Saturdays, nor most holidays.(10) Factors considered in determining the daily condition val~esincluded (1) the amount and duration of sunlight, (2) ~hepresence and duration of wind, and (3) temperature 'duration' ~ndhumidity. These factors were not given specific weights.

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1. All "0" values were converted to "missing".2. A reported minimum temperature of 82 degree F. tor

Wednesday of the week of 9-1-78 was changed to 62 degrees.3. All temperatures were converted from degrees Fui;r,:r:L:.it

to degrees Celsius.(12)4. Weekly averages of nonmissinL, condition vcilues unci of

:llaxinlumand minimum temperatures, os well as count::; of the nLd. L,:rof nonmissing values in each weekly average.

"FRU IT" con ta ins the foIl ow ing da ta for wee ks 2.6 t. hI;" Ig t:109 :

1. Number of fruit set.2. Average weekly condition and

minimum temperatures.3. Extreme condition and temperature4. All of the above for the previous

average maximum jncvalues for the ~L~~.week.

"LAGS" contains the following data for weeks 34 thr'out)· 'i09of the observation period:

1. Weekly sales, in pounds of tomatoes.2. The number of fruit set 8, 9, and 10 weeks earlIer.3. Three week cumulations of weekly average conoi::'i,";"),

average maximum temperatures, average minimum temperatures, ~ndof the weekly differences between average maximum and minI~umtemperatures. The periods of cumulations were:

(a) The first three weeks before harvest,(b) The three week period before that, and(c) the three week period before the second per'ied

(i.e. 7-9 weeks before harvest).4. "Average weights of fruit sold" computed by dividin(. ~nE:

sales for the week by the numbers of fruit set 8, 9, and 1Cweeks earlier.

5 . Averages of the m inim urn 0 nd rna ximum daily tenI p E:: r':Lon,:::,for the current week and for each of the nine preceding ~ee~~.

-------- -~--- - ----------~-------_._-_.._.- - -----_._- ------(11) See Table 1, Appendix for a complete listing of the (oiteddata.(12) Aside from the above, all values were accepted as rec~iv~a.

- 16 -

H<ld TSf T

ft:f'-I'-LY," U (vI H t R

1 to ."If 1 t. . F It."W 1l,yip 1 f;: 1.\ ufo

l ----- L ----- L ----- C ---L- ---------1., I, 1 J ]'1 1'1 IJ v! 'I ~ I I j '-, t>1

1 A 'J r A ' ~ A r , 1 A " 1 A

LJ !j X I) j X li I" X. \J ,J r.. ~ I\j X

--------- --------- --------- --------- -------------, I).")'" '( 1 j t jl)" Y

HttK .-------- ------- ..__l:.WJ..l..tii 1 t.:' P , t.' f'

L .---- L ---- ..iJ rtlJLA Y1 U '" r , I 'I r.·,

,\I 1 A A

MU~llJ.\!"'tt-{ l.i It It. ' , ;, ,...._______________________________________________ n --------------------------------------

--------.-~-----------------------------~~--------------------------------------------------

b-11-7 7 ..l.i.._.3 u 1 l~ i1 7 l.L.H I l~ 32- .1:1 1~_iiL a .__ a _.•. ____2..a6 .1~J.u.jU. 8 ~20,~~(Jb-2~-7 7 1..•51 (J 1 4 31 M 14 31 7 1~ 51 0 1~ 30 • b.~ 14.4 3u.8 1(n,2~(;

._7~n~1 -- .7 1"1 31 t! 1 .3 .H I 14 .H 7 1 ,~ .)1 7 114 .32 • a • (;lad 14. 1 'su,9 17d.24()7- tj-7 • , • ':> 14 .~II 7 1 S 2M ~ 14 ~~ t> 14 ~7 • 5.~ 14.b ,cb.b - 109,"~O

_..1.•15-1 'i • a 4 l~ ~'-/ 4 114 21-) 4 1n 28 ~ 14 t!.h • • 5.U 14.9 ~b.l 175,120 -- -----.---- -

7-22-7 '4 17 29 ~ 1~ c'} 0 10 2~ 5 14 27 5 10 ib • • ".0 15.3 2tj.2 100,()407-29-7 1_ 1.JL~2. __ l. Li ..2.'-/ l;;l L~·LJ.L .. _Q . l~ ..1~ LI 14 t!.Q .1- . a. a,. _ ~.a iJ._l S.•.1__~9. \L. 1LQ..L9 ()08- rs-7 b 10 ~H ~ 14 27 " 1b 28 7 17 .H 7 17 31 • 0.0 1~.CS 2Jj.9 104,940l'j.-l.2 ••7 ~ 17 3U "1 1b 32. h 19 31 0 11; ~v 3 l~ 24 • • 0.4 17.8 2'1.0 \07,1~u6-19-7 ~ 17 2d 9 17 .so,) t; 19 32 d 10 34 q 17 52 • • • CS.b 10.9 ~2. 3 176,700

__ 8.~b" 7 b_1~ 32. tl 14 c?Q J 1-1 2rJ. 9 14 .B b 14 2d • 0,8 14.2 24.7 1RQ, 0H 0 .___--.--- -- ---_.- -

9- 2-7 7 13 31 7 1.5 31 0 14 31 7 13 ,;~ 7 14 31 • 0.8 1';.b .H .0 Id4,8dO9- Cf~_- Q.--1..!L...ll.. - .~li.! J\j ~ L'L.2b -~. 1.L 3() Q. 1~_ Zit .. __. .A_._ •... ".A .. Q.... Z_J.l~ • 9._~ 9..L1i._.l.l~. 2 d9

9-10-7 y 114 .H b 14 2'1 b 14 29 7 1~ 2'1 ~ 14 27 • • • b.4 14.2 2~.1 192,4Bu____.___~ .•.~~L .. ~_l't ..iO I l'i 2f..J I 14 2.'i 5 lLi 27 Q 1'4 2.7 • • .. 0.lJ.14.1 ~b. 7 2l) 7 • 4 2 O__~ ____ u. __ • _________ u_

9-3U-7 b 1L4 31 S 14 3u 5 14 29 4 14 c!.9 r; 13 29 • • • 5.0 14.U 29.7 200,42U_ . __1Jl.••_l••1 . 5 1j 2.f..J ~ 1t! 2.d , 1<+ 2Q _2. 1.4 ,b '.) 14 ?7 • • I. C;I.~ 1~1.0 i'~.LH 15b.400._

lO-1l.1-7 b 1~ 24 ~ 14 2,9 5 14 28 b 14 28 5 14 27 • • • 5.l.I 14. 1 2";.5 178,70010 - 21- 1-..3...l ~L..iu.. .. I.l. l~ 2.? __n.~~1.ti_ .2.~ -.- Q 15 29 ____q nl~ .-'Q._._~_. L_ ..~ 1._~_1_~.•_'!. __ ? H. 4 1.04..1.7 0.0lU-cd-7 4 13 i'9 '; 13 20 2 1l.j20 7 14 t!.9 C 1 ~ 26 • • 4,0 15.7 27.0 175,540.1.1-.. ~7 . ~. l'i i''t 7 14 2. 'J ';) 14 ~~ , l'~ ~4 7 14 ~q • • 5.2 l4.l. i'7.9 _149,~20 . ------------.

11-11-7 ~ 9 24 b 15 CO 7 13 29 7 1~ ';u 0 14 30 • b.2 12.4 2"!.3 171,oUO-- . 11-1~~7_- 0 12 .H 2 14 ,7 ;) 1'1 ,7 ., 15 2.9 H 12 31 • 4.H 12,9 ?9,0 1HH,5UlI._ -----_. - ---

11-2~-7 t) I1 31 tj 11 ~2 0 12 31 • • • • • • • • • 7 .~ 11•3 31.3 191,3!j012- i'.-7 _....J:L.iL . .3 2. ._ . I 11 j:j _~. J2._~_ 1_11.j 1 4 13. ~.L .---.- .•. __ ..I. __ Q..I.'i._lhL.2.9• 7_L9.~ ~_/~O

12- 9-7 7 11 33 tI 11 .B 4 13 29 6 11 32 7 1 1 51 • • b.4 11. 1 31.7 195,10U.j~-..l o-l. 2 11 ;)} l 11 ~, ~ 11 )1 ., j~ 31 2 11 ~s • I. .. .? • U .11 ,2 311,3 209,1)0(1. ____________

12-23-7 • • • • • • • • • • • • • • • • • • • • 172,940.___ J.-,--..JQ- 1_ . • t:) 3~ 0 II 2/:'0 4 12 27 ~ 13 c!.9 I H 31 ! , 5,5 10 .3 29,3 14b,580-- ! ..- -- ---- --~--- ------ ..

1- 0-7 • • • ,) 12 ~1 3 1u 3U 4 7 2b 7 b 31 • • 4.3 9.3 2-l.4 14Q,bOO1·1..~-7 c; .Jt .J 1. _ . .tLJ._~.~, _..~Ll.i~. 0 7 .?J b '; 30 , b ~.q 30,7 14Q,~CSO

- . - __ .. ____ .___. _.__ .l-_~ -...I..--~