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r I r I I I , 1 ANALYSIS cg HAWAII I ( GREENHOUSE TOMATO DATA I [ I I I I I l I Hawaii gricu~tural ep<;>rtmg Nice ~ Hawaii Department of Agrrculture US. Department of Agriculture ANALYSIS OF HAWAII GREENHOUSE TOMATO DATA Prepared By: Fred B. Warren, Senior Math Statistician United States Department of Agriculture Statistical Reporting Service, U. S. D. A. Statistical Research Division Yield Research Branch for Hawaii Agricultural Reporting Service A cooperative function of Hawaii Department of Agriculture Marketing & Consumer Services Division United States Department of Agriculture Statistical Reporting Service ANAL YSIS Of i1l1.1 '1<1 GREENHOUSE TOMATO DATA. I By Fred B. Wa rren, Statistical Research Division, Economics and Statistics Service, U. S. Department of Agriculture, June 1981. ABSTRACT One hundred seventeen weeks of temperature and greenhouse tomato condition data were evaluated to identify factors which might be related to weekly sales and fruit set. Prototype moaels were developed from the given data both to determine the types of variables which would be most useful and to determine the possible gains in precision which might be obtained. The principal findings of this evaluation are that: data of the type evaluated can be used to develop reasonable forecast and estimation mod~ls for numbers of fruit set, for the amount of saleable fruit, and for the average weight per fruit, and that the numbers of fruit set and average weight of fruit at maturity responded differently to different levels of maximum and minimum temperatures 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 Agriculture. The views expressed herein are not necessarily those of ESS or USDA. * * * * ************************************************************* - i - TABLE OF CONTENTS ANALYSIS OF HAWAII GREENHOUSE TOMATO DATA INTRODUCTION . ANALYSIS Initial Analysis Weekly Plots of Fruit Set and Sales Daily Condition and Temperature Data: Number of Fruit Set: Sales . \.,r e i g h t per Fr u i t APPENDIX DATA . 1 1 1 2 2 3 5 8 11 15 15 - ii - ANALYSIS OF HAWAII GREENHOUSE TOMATO DATA INTRODUCTION The data Gsed in this analysis was compiled by a commercial greenhouse tomato grower in Hawaii. It was then passed to th8 Hawaii State Statistical Office (ESS-Statistics) for analysis, particularly to define those factors which related specifically to production. This task, and the data, was then referred to the Yield Research Branch, Statistical Research Division. Difficulties with the data included the following: (1) Estimates of the number of fruit set and of sales were recorded by weeks for the entire operation, even though the actual areo in production varied widely over the 117 week period; (2) Estimates of 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 formula which included the effects of sunlight, wind, temperatur~ and humidity, the actual weights used were not recorded. ANALYSIS The analysis was directed both towards determinir.g Ule possibility of using the observed temperature and "conditlGn" data to predict the components of production, i.e., the number of fruit set and the average weight per fruit at harvest, and towards 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 and duration of wind, and (3) temperature "duration" and humidity. These factors were not given specific weights. - 1 - 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 actual numbers which, if not unbiased, at least had a constant (13S throughout the entire period. 2. The number of fruit sold as a proportion of fruit set W;l~i c.;on:;Ltn1. thr'oughout U1e enti re period. 3. The i.lnlO un t 0 f t i mer e4 u ire d for the f ru it tom d t ur e was constant throughout the entire period.4. All plantir.gs were of the same size and stayeo in production for the same amount of time. 5. The reported condition figures were basea upon .ome unchanging objective criteria. 6. The reported temperatures were uniform for ~ll greenhouses in the complex. Because the reported numbers of fruit set are estl~ates de riv ed fro m co unt son "repre sentat iv e" pIa nt s , any cor re le:, t 1. c n or regression analyses involving the number of fruit set wil~ not be as good as if the actual counts, even for small units, coulo have 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 the pounds of fruit sold, over time. (b) Correlating daily reports of condition, an~ of maximum and minimum temperatures over time. Weekly Plot~~uit S~_~d Sales Because the actual number of plantings in production at any time was not given, plots of the weekly fruit set and sales cata were used to determine the period of time during which the n~mber of plantings, as indicated by the data for fruit set and sales, would be comparatively stable. As shown in Figure 1, there WaS a rapid increase in the number of fruit set each week from week 1 until about week 24. This resulted from a rapid increasE in total plantings during this period. Then, aside from irregularities in fruit set and sales which may be related to the weather, the number of plantings in production appeared to be somewhat constant from week 25 through 109. However the number of 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 drastic reduction in the number of plantings in production during WEeks 110-117. Therefore, the analysis to relate the observed vJlues of condition and of temperature to the number of fruit set was limited to the data for weeks 25 through 109. Also, since there - 2 - I appears to be about an 8 to 10 week lag between fruit :Jet. and sales, the analysis to relate condition and temperature d2ta to ~ctual sales was limited to weeks 34 through 109. PLOT OF FRUIT.wEEK PWT OF SAlESOWHK 5'''801. S'''801. useD IS F .....•.. USED 15 5- FRuIT ll~OOO I I • I I I I lGOOO 0 • I I I I 1UOOO • I I I I l~OOOO • I I I I 1HOOO • : j-. ;; r~ .1\. t 1\ f ! ~ f 1ססoo0 • I I I I ~ r. I I I I J~OOO • ?/¥ ~ 1:: \[F~ ~ ~ooo0 I I I I • I I I I l~OOO • I I I o • I - --.- --+--+ I bill. --.---.---+---.--+--.---+---.----.--+----+---~--+---.---+--+---+--+--+--+--+-ZI i6 31 3b .1 '"" 51 ~. 61 66 fl 16 BI Il6 01 06 101 106 III lO£EK II. Figure wef:'ks. 1: Numbers of frui t set and pounds of tomatoes sol (, I l'J Daily maximum and minimum temperatures were grouped by ~~c correlated with condition codes. This was to determine how well they were related (See Table 1). Both daily and weekly average data were also plotted and regressed over time to determine if there appeared to be any long term factors in the data. (The effects of any seasonal cycles in the data would appear to be minimal, since the first and last 14 weeks of the study period overlap the months of November through February.) The principal findings from this stage of the analysis ~Iere the highly significant downward trends over time for (1) reported daily conditions, (2) daily ranges in temperatures, and (3) reported maximum daily temperatures. There was also a very high positive correlation between the daily reports of condition a~d the maximum daily temperatures. That is, high daily maximum temperatures tended to be associated with high condition values. - 3 - Table 1: Coefficients of correlation (r) between reported Gully condition 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) Temperature Varicble Time Condition Maximum temperature ~:ini!llum temperature r p(r=O) r p(r=O) r p(r=O) r Time 1 •000 0.000 -0.296 <0.001 -0 .112 0.007 0.156 <0.001 Condition -0.296 <0.001 1 •000 0.000 0.638 <0.001 -0.249 <0.001 Maximum -0.112 0.007 0.638 <0.001 1 •000 0.000 -0.092 0.028 0.156 <0.001 -0.249 <0.001 -0.092 0.028 -c. 17 4 <-G.OOl C.638 <0.;:)01 C.038 <0.001 p(r=O) 1 .000 0.000 -c .cu:1 <0.001 Although still highly significant, the correlation bet'vleel! crie reported daily conditions and the minimum daily temperatures WaS smaller than for condition versus maximum temperature. Also the correlation of condition with minimum temperatures was negative rather than positive. This implies that low minimum temperatures tended to result in high condition values. The negative correlation between minimum temperatures, and both the maximum and daily range of temperature may be associated with periods of clear skies. Clear skies would be associated with a gredter degree of nighttime cooling and more sunlight during the day--hence higher maximum temperatures and higher daily condition values. Normalized weekly average condition and temperature values were plotted over weeks. These plots (Figures 2a and 2b) indicate that (1) there was no significant seasonal pattern in the fluctuations of the daily maximum temperatures, 2) the weekly average condition values did follow the pattern establishec by the weekly average high temperatures, but (3) that there was a significant seasonal pattern in the daily minimum temperatures. Means, standard deviations, and maximum and minimum values of the reported daily values are in Table 2. - 4 - Table 2: Simple statistics for daily reports of maximum and of minimum temperatures, and for numbers of fruit set, of total sales, and of weights per fruit, Hawaii greenhouse tomato 2-3-79. Mean Variables Condition Temperature:* High Low Range Fruit set per week, weeks 24 to 101 Sales per week, weeks 34-109 5.277 29.44 12.95 16.49 (000) 176.9 47.81 Standard Error 2.07 3.52 2.45 4.48 15.67 9.77 C. V. condition arJo of weekly val ue~> of derived ave-rage d a t a, 1 1 - 7 -( l' to Mi nimum ~'ic..l/~ H;t.;[;, -----------------------------------------------------------_._-~-(% ) 25.9 11 .9 19.0 27.3 16 4 4 146.58 29.18 v -------------------.-------------------------------------------~--' 41 1S 31 .54 8.9 20.4 L:C: ,; (000) 69.31 Average weight per fruit 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 the average number of fruit set 8 and 9 weeks earlier. * ** by This portion of the analysis was limited to the data lrom weeks 25 through 109. This was because the first 24 weeks apparently represent a period of buildup in production, and til~re were no observations for numbers of fruit set during the last 8 weeks. Factors considered in attempting to model the number of fruit set each week were the average and extreme temperaturesr and the condition values both for that week and for the previous week. The first portion of this analysis was to determine if the same trends observed over the entire period for reported dally condition and temperatures also held for the abbreviated subset of weekly averages. After adjusting the regression coefficients for differences in the numbers of observations, the data in Table 3 indicates that there were essentially no differences between the two sets of trends. - 5 - U"D 1 • I I I I I I I I I -,laD _laD ~ITIOII 1ICJ1 ~_ '-1. 11C-•••••••••• IlllIOI. II S , • I • I I I I • -a • I • I • I I I I I I I I I I -I • I • I I I I I ..• --+---.-.--+---.--.-.---.-~ 1.1l162116UJ6 41 • 46 • •• Figure 2A: Normalized weekly temperatures, by weeks. UCJlD I I •• conditions aoa a06 II a 116 average almI1TICII LOll TIMP__ and maximum , • I -.IID IIlDW.UID · I I I I I I • -a • I I I I I I I I I L · • I I •t C -, -I V · f • I I I I I I ..• .., • I I I I • I ---.--....-.-- . , • I II 16 2l • • I n +--t ,. 4' t 46 t 51 •• ,. 61 .11I I --+_..-_...--•..--..4-....--. •• n ea •• u •• 'PI. '0' , t--.-..-,•• au au Figure 2B: Normalized average temperatures, by weeks. reported conditions and minimum - 6 - I 1 I Table 3: Coefficients of correlation (r), probabilities of nonsignificance (p), and regression coefficients for daily condition and temperature observations over time for 117 weeks vs. weekly averages for only weeks 25 through 109, Hawaii Greenhouse Tomato data, 11-7-76 to 2-3-79. Type of Observation Variables Daily (117 weeks) 569 r b Maximum temperature Minimum temperature r p b r p b P Weekly Averages (weeks 25-109) 85 -0.471 <0.001 -0.025 -0.131 0.235 -0.0090 0.153 0.161 0.015 Observations Condition -0.296 <0.001 -0.003 -0.112 0.007 -0.0016 0.156 <0.001 0.0016 Given that there were no differences in the trends for either condition or for weather, the next step in the analysis was to use a stepwise 'max r-sq' regression procedure to identify the variables which would be most useful in modeling the number of fruit to be set in any particular week. Variables evaluated in this analysis included both the linear and quadratic effects of maximum, minimum and average high and low daily temperatures and condition reports for both the current and for the preceding week as well as the number of fruit set the previOUS week. For the range of temperature values observed, the best model (best in terms of having the smallest residual mean square error) for this purpose would contain the variables listed in Table 4. This model has a coefficient of correlation (r) of 0.64 and the standard deviation of the residuals is 12,538. Given the overall weekly average number of fruit set of 175,838, this implies that about two out of every three predictions from this model would have been within 7.2 percent of the actual number. With respect to the overall mean, this model would have a relative precision of about 0.65.(2) (2) The relative precision of one model - 7 with respect to another Table 4: Variables for estimating weekly numbers of fruit with regression coefficients and F-values, Hawaii greenhouse tomato data, weeks 25 through 109. set, ----------------------------------------------------------------b Variable ----------------------------------------------------------------Intercept -144909.3 Average condition last week 340.11 --squared Highest minimum daily temperature 1503.23 (Celsius) observed this week Highest maximum daily temperature 1275.30 (Celsius) observed this week Number of fruit set last week 2.256 -- linear - 0.000005 -- squared 10.45 7.63 2.85 1.85 1.34 ----------------------------------------------------------------The functional relationships represented by this group of variables could be defined as follows. First, there is a very strong positive and non-linear relationship between growing conditions the previous week and the number of fruit set during the current week. Second, and within the range of temperature values observed, there is a strong positive and linear relationship between high minimum temperatures and the number of fruit set during a particular week. Also, the regression procedure rejected weekly average minimum temperatures in favor of the highest daily minimum temperature. High maximum daily temperatures are also desirable but not as much as high daily minimum temperatures. Finally, there is an overall positive non-linear relationship between the number of fruit set during the previous week and the number of fruit set during the current week. Sales The second stage of the analysis was to cumulate weekly averages of indicated conditions and of maximum and mlnlmum temperatures. These were lagged over both weekly and three week intervals. The lagged three-week cumulations were also squared. Therefore, the augmented set of observations for a particular week included the sales for that week, the linear effects of the weekly temperature and condition values, and both the linear and quadratic effects of the cumulated three-week values. The is expressed as the two models. In this between the reported estimated by the model weekly deviations from ratio of the variances of the errors of the case, the variance of the differences numbers of tomatoes set and the number would be divided by the variance of the the overall mean. - 8 - augmented (lata set also included the averiJge weekly llumtJcl ,;1 frui 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 and the tail off in production during the final 8 weeks, this analysis 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~6 the tenth week before harvest (r= 0.444), the average condit.l~-,ll 4 to 6 weeks before harvest (r= -0.384), the range of average d~ily temperatures during the tenth week before harvest (r= 0.382), the week itself (r= 0.378), and the square of the average condit~on during the fourth to sixth weeks before harvest (r= -0.377).~3) With 76 observations, all of these correlations are statistic~lly different from zero at the .001 level of probability. Howcve~ the coefficient of correlation for the linear component of che average condition 4 to 6 weeks before harvest is only slibhtly larger than the coefficient for the quadratic component. 1t;15 indicates that the quadratic component really is not imporc2nt. 2. Although the individual correlations are hi~hly significant, statistically, individually they are not lGrge enough to support a forecast model. Therefore the analysis vias taken into a stepwise "Max-R-sq" multiple regression to sort out the variables which would interact to form the most efficient model. (The best model is defined here as being the one for which the sum of squares of the differences from the regres~i0n surface is least.) The best multiple regression (Table 5) had a R-sq of G.73 and a standard deviation of the differences between actual and predicted weekly sales of about 5,540 pounds. This computes ~~ a relative standard error (CV) of about 11.6 percent. Thi~) elTlT is only about one-half as large as the 20.4 percent CV com~uted for the weekly deviations of weekly sales from their own mean. The relative precision of the model with respect to the overdll mean was 0.32. An apparent weakness of this model lies in the small contribution to the estimated sales which comes from the number of fruit set. This may only indicate that the tomato plant tends to compensate for small fruit sets with larger tomatoes. (3) The rationale for the negative correlation between weekly sales and the average 'condition' 4 to 6 weeks earlier could be that, since there was a high positive correlation between the daily condition reports and the maximum daily temperatures, the negative correlation would indicate that tomatoes at that SlJbe of maturity develop better with relatively lower temperature~. - 9 - Variable ----------------------------------------------------------~---,. b Table 5: Variables for estimating weekly sales of tomatoe~, w~t,L regression coefficients and F-tests of their significance, fl<H-:al.i tomato greenhouse data, weeks 34 through 109. _.- ---------------------------------------------------------------~-~ Intercept -1878077.224 0.0589 for _ ~.26 • 1 .2 Number of fruit set eight weeks before harvest Sum of average weekly conditions 7 to 9 weeks before harvest Sum of weekly average maximum temperatures for 1 to 3 weeks before harvest 4 to 6 weeks before harvest 7 to 9 weeks before harvest Squares of sums of weekly average conditions for 1 to 3 weeks before harvest 4 to 6 weeks before harvest weekly high average temperatures for7 to 9 weeks before harvest weekly low average temperature for 1 to 3 weeks before harvest 7 to 9 weeks before harvest Weekly average high temperature eighth week before harvest tenth week before harvest Weekly average low temperature tenth week before harvest for the -1653.529 1910.637 -1285.699 41103.464 c ~,. '\ 1 lc.22 1 "~ • 79 -41.388 33.300 -220.625 9. 129 -12.641 1033.110 1323.894 1 b. • L,4 .97 69 21 .9C L:::' ~;3 ( .65 ~~• f) S for the ----------------------------------------------------------~-,----- 839.901 I • (() It should be noted that the most important variables in •.. Le multiple regression equation, as defined by the "F"-values, are not the same variables which had the highest linear correlati~ll. Also, one variable could be said to appear three times in that the weekly average high temperature for the eighth week is also included in the linear and quadratic effects for the su~ of average maximum temperatures of weeks 7 to 9 before harvest. The model coefficients (b's) listed in Table 5 indicateL.llat maximum production would result from the following combinati0n cf factors. 1. A maximum number of fruit were set. Within the range of temperatures reported, both maximum and minimum temperatur_~ 10 - 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. tIle observed conditions should be high. 4. For the final three week period (1 to 3 weeks beIGre harvest), daily maximum and minimum temperatures again shoulc be high and the observed conditions should be low.(4) Because the above model requires condition and temper2t.ure data up to the week of harvest, it can be used only to estiffiate production for the current week. However, marketing specialisLs, etc., could reasonably want to predict production in advance of actual harvest. Therefore a similar analysis which excluded ~ll data not available within three weeks of harvest was conducted. This was both to illustrate what might be done and to point cut the loss of precision which should be expected when using ~ less than full season model. The variables and regres~ion coefficients for such a model are listed in Table 6. As expected, the R-sq for this model is smaller (0.61 vs. 0.73) and the 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.. -IL.1lit L Since no actual weights per fruit sold were included with the data, weekly average weights per fruit sold were computed from the reported weekly sales for weeks 11 through 117 and from the reported numbers of fruit set 8, 9, and 10 weeks earlier. Factors considered in attempting to model the average weight of fruit at harvest included the lagged three-week cumulatior:~ of condition and of temperature plus the reported numbers of fr~it set 8, 9, and 10 weeks before harvest. A stepwise 'max r-sq' regression analysis of the above Uata showed that the highest correlations were obtained when the dependent variable was weekly sales divided by the reportea number of fruit set 8 weeks earlier. The best model (again, best from the standpoint of having the smallest residual mean square) used thirteen variables and resulted in a R-sq of 0.77. The standard deviation of the residuals was 0.031 pounds. Variables and regression coefficients for the 'best' model are listed in Table 7. ------------------------------------- --. - --(4) Considering the overall high positive correlation betvleen maximum daily temperatures and condition, the indication that temperatures should be high but that condition should be low hints at some type of complex interaction. 11 - Table 6: Variables for predicting weekly sales of tomatoes tnree weeks before harvest, with regression coefficients and F val~es, Hawaii tomato greenhouse data, weeks 34 through 109. ------------------------------------------------------------.-.---Variable Intercept Number of fruit set eight weeks before harvest Weekly average high temperature tenth week before harvest Weekly average low temperature eighth week before harvest for the b ---------------------------------------------------------------2050694.760 -0.0639 2071.507 for the 1 .32 1::;.5, -3268.936 for 26.07 Ic.:;8 Sum of average weekly conditions 7 to 9 weeks before harvest -7691.265 44751.807 4365.578 Sum of weekly average maximum temperatures for 7 to 9 weeks before harvest Sum of weekly average minimum temperatures for 4 to 6 weeks before harvest Squares of sums of weekly average conditions for 7 to 9 weeks before harvest weekly high average temperatures for 7 to 9 weeks before harvest weekly low average temperature for 4 to 6 weeks before harvest 168.865 -240.503 -48.768 0.02 -----------------------------------------------------------_._---The mod e 1 co efficien t s (b' s) lis tedin Tab 1e 7 w 0 u 1d i [" 1y ~ that the largest (heav iest) tomatoes would resul t fror;.thE following combination of factors. 1. The number of fruit set 8 weeks earlier is relatively small. In fact, the fewer fruit set, the larger they will be. 2. Within the range of temperatures reported, ~igh temperatures, both minimum and maximum, from 8 to 10 weeks before harvest are desirable.(5) 3. For the first 3 weeks after fruit set (7 to 9 weeks before harvest), high daytime temperatures and low nightLime temperatures are desirable. The response to higher daytim~ (5) Interestingly, the data presented in Table 5 indicates that higher temperatures during this period are conducive to larger numbers of fruit being set. This would appear to be at varicc.l1ce with 1. 12 - I t I I I 1 Table 7: Variables for predicting average weight of ton,C:.iL,ue::.; (pounds per fruit) at harvest, with regression coefficients :ind F-tests of their significance, Hawaii tomato greenhouse oata, weeks 34 through 109. ------_ .. --- -----------------------------------------------------~ b Intercept Number of fruit set eight weeks earlier Sum of average weekly 7 to 9 weeks before conditions harvest for -10.47702 -0.00000099 -------------------.---------------------------------.------.----. 1 1 .35 16.50 I I Sum of weekly average high temperatures for 1 to 3 weeks before harvest 4 to 6 weeks before harvest 7 to 9 weeks before harvest Sum of weekly average low temperatures for 7 to 9 weeks before harvest Squares of sums of weekly 1 to 3 weeks 4 to 6 weeks sums of weekly 7 to 9 weeks sums of weekly 1 to 3 weeks average before before average before average before 0.011880 -0.007391 0.222322 29.03 12.7:, 18.17 -0.005900 14.6S conditions for harvest -0.000236 harvest 0.000189 high temperatures harvest -0.001192 low temperatures harvest 0.000053 0.005822 0.008181 0.006056 9.85 5.05 17 . 13 22.441 Weekly average high temperatures 8 weeks before harvest 10 weeks before harvest Weekly average low temperatures 10 weeks before harvest 2.6~ [..29 2.42 temperatures is non-linear, tapering off increase. 4. For the second three week period (4 to harvest), desirable factors are low daytime high condition values.(6) as 6 weeks eel (,re temperatures:":Ld ---------- --------------- --------_. -- ---- -- -.- --(6) Considering the high positive correlation between re~orted condition figures and the daily maximum temperatures (Table 3), this particular combination appears odd. 13 - 5 . For the fin aI th ree vJ eek per i 0 d (1 to 3 wee k s (; I u n:: e harvest), desirable factors are a combination of high maxind ..• ond t.i minimum temperatures with low condition values. \~ i let h e ab 0 ve ana 1y sis did inc 1udeb 0 th the 1i ne :Jt' , ! Li h quadrCltic effects of the observed and derived vari8blE's, then: was no attempt to examine the possible "threshold" effE:;ct:oof extreme daily and/or weekly temperature values. (7) (Thel.:;,ta does not suggest that any "threshold" temperatures were observed.) The varic:bles listed in Table 7 are virtually the samE: "rJeCc. which appear in Table 5. Also the relative importance, as measured by the computed "F" statistics, of the seven hignest ranking variables in each model is identical. Therefure, considering that the the multiple R-sq's of the two models are very close (0.77 for weight per fruit vs. 0.73 for total sal~s), there would seem to be little advantage in computing prGb2SiE sales as the product of separate estimates of the number of lr~it set and the average weight per fruit. ----- ----~----- --.---------- - - --_._- -- ------ ----------- - (7) "Threshold is defined here as being a level at which nil plant's response to its environment becomes asymptotic. l:"or example, the temperature may become too high or too low for any blooms to develop. 14 - I I I APPENDIX DATA The data set obtained fronl the Hawaii State Stc:tistical Office contained the following information for 117 consecutive weeks of greenhouse operation. 1. Month, day and year for the FRIDAY of the calendar ~eek in 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 growing conditions(10) in the greenhouses. Daily observations were recorded Handay through Saturday. Plantings reportedly were made at two week intervals. i~ IS not known how long a particular planting stayed in production or how many plantings were made. The data also did not indicate if all the plantings were the same size. The basic data, as received from the Hawaii State Statistical Office, is resident on the USDA Washington Computer Center (ViCC) a san 0S f i1e , DSN = RAD 14 •TOM ATO. DATA . The rei s a 1so 8 t ! d' ec member 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 editing changes:(11) ---------.--~- ---_._---~---- ----------- ----_ _--- (8) '~umbers of fruit set' were extrapolated from count~ of 'pea-size' fruit on ten 'representative' plants Hl ;:3ch greenhouse. (9) No observations were taken on Sunday, any time the week of 12-23-77, most Saturdays, nor most holidays. (10) Factors considered in determining the daily condition val~es included (1) the amount and duration of sunlight, (2) ~he presence and duration of wind, and (3) temperature 'duration' ~nd humidity. These factors were not given specific weights. .. - 15 - 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 :llaxinlum and minimum temperatures, os well as count::; of the nLd. L,:r of nonmissing values in each weekly average. "F RU IT" con ta ins the foIl ow ing da ta for 109 : wee ks 2. 6 t. hI;" I g t: Number of fruit set. Average weekly condition and minimum temperatures. 3. Extreme condition and temperature 4. All of the above for the previous 1. 2. average values week. maximum for the jnc ~L~~. "LAGS" contains the following data for weeks 34 thr'out)· 'i09 of 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, ~nd of the weekly differences between average maximum and minI~um temperatures. 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 1C weeks earlier. 5. Averages of the m in im urn 0 nd rn ximum daily tenI p E:: r':Lon,:::, a for the current week and for each of the nine preceding ~ee~~. --------~ --- - ----------~-------_._-_.. _.- - -----_._- -----(11) See Table 1, Appendix for a complete listing of the (oited data. (12) Aside from the above, all values were accepted as rec~iv~a. 16 - __l:.WJ..l..tii .iJ rtlJLA Y1 --------.-~-----------------------------~~-------------------------------------------------ft:f'-I'-LY t HttK .-------- ------- .. --------- --------- --------- --------- ------------f;: 1l,yip 1 t. . It."W 1 1 P ----- ~ ---L- -------------------- . .---'-, , I).")'" '( 1 j t jl)" Y ," U (vI H R t.:' , t.' f' to ."If F 1 1.\ ufo L L l L L C U ,\I '" r , I 'I r.·, 1., LJ I, 1 J ]'1 1'1 IJ ' v! 'I I Ij t>1 H<ld T 1 It A It. MU~llJ.\!"'tt-{ b-11-7 l.i 7 '... , ;, ,. i1 A 1 !j A 'J r j A ~ I" A r , 1 ,J A X I) X n li X. \J r.. ~ " 1 I\j A Sf T X _______________________________________________ -------------------------------------- ~20,~~(J 1(n,2~(; 14.4 3u.8 0 1~ 30 7 1~ 51 (J • 1 4 31 7 1..• 51 b-2~-7 (;lad 'su,9 17d.24() 14. 1 7 114 .32 7 1 ,~ .)1 • a • 1 .3 .H t! 31 ._7~n~1 -- .7 1"1 5.~ 14.b ,cb.b - 109,"~O 14 ~7 t> ~ 14 ~~ • 14 .~II ':> 7- tj-7 • , • 175,120 ~b.l -- -----.---- ~ 14 t!.h 4 1n 28 4 114 21-) 4 l~ ~'-/ • • 5.U 14.9 2tj.2 100,()40 _ . .1.•15-1 a 'i • 15.3 5 10 ib 5 14 27 • 0 10 2~ • ~ 1~ c'} 7-22-7 '4 17 29 0 a,. _ ~.a iJ._l S.•.1__ 9. \L. 1LQ. .L9 () ~ LI 14 t!.Q a. l;;l 1~ __ l. Li ..2.'-/ L~·LJ.L .. _Q . l~ .. 1_ 1.JL~2. 7-29-7 1~.CS 2Jj.9 104,940 0.0 7 17 31 7 17 .H 1b 28 • ~ 14 27 b 10 ~H 8- rs-7 0 11; ~v h 3 l~ 24 "1 19 31 1b 32. • • 0.4 17.8 2'1.0 \07,1~u l'j.-l.2 ••7 ~ 17 3U q 17 52 d 10 34 t; 19 32 9 1 7 .so,) • • • CS.b 10.9 ~2. 3 176,700 0 .___ ~ 17 2d 6-19-7 1 R Q, 0 H 0,8 14.2 24.7 --.--- -- ---_.9 14 .B b 14 2d J 1-1 2rJ. b_1~ 32. • tl 14 c?Q __ 8.~b" 7 Id4,8dO .H .0 7 14 31 7 13 ,;~ 14 31 0 • 0.8 1';.b 7 1.5 31 7 13 31 9- 2-7 .. Q.... Z_J.l~ • 9._~ 9..L1i._.l.l~. 2 d 9 Q. 1 ~_ Zit .. -~. 1.L 3 () ~ L'L.2b 9- Cf~_- Q.--1..!L...ll.. - .~li.! 192,4Bu ~ 14 27 7 1~ 2'1 y 114 .H b 14 29 b 14 2'1 • • • b.4 14.2 2~.1 9-10-7 2l) 7 • 4 2 O__ ~ ~b. 7 0.lJ.14.1 Q 1'4 2.7 5 lLi 27 I 14 2.'i ____ ~ .•. .___ ~~L .. ~_l't • • I l'i 2f..J ..O i 200,42U r; 13 29 14.U 29.7 4 14 c!.9 5 14 29 • • • 5.0 S 14 3u b 1 L4 31 9-3U-7 C;I.~ '.) 14 ?7 _2. 1.4 2.f..J 1<+ 2Q 1t! 2.d ~ _ . __Jl.••_l•• . 5 1j 1 1 • • I. 5.l.I 1~1.0 1 i'~.LH 15b.400._ 2";.5 178,700 14. 5 14 27 b 14 28 5 14 28 ~ 14 2,9 • • • b 1~ 24 lO-1l.1-7 1.04 0.0 . .1.7 L_ .. 1._~_1_~.•_'!.__ ? H. 4 ~ q n.~~1.ti_ .2.~ -.- Q 15 29 ____ nl~ .-'Q._._~_. 10 - 21- 1-..3...l ~Liu.. .. I.l. l~ 2.? __ .. 175,540 4,0 15.7 27.0 C 1 ~ 26 7 14 t!.9 '; 13 20 2 1l.j20 • • 4 13 i'9 lU-cd-7 5.2 l4.l. i'7.9 _149,~20 ------------. 7 14 ~q ';) 14 ~~ l'~ ~4 2. 'J 7 14 • • .1.1-.. ~7 . ~ . l'i i''t 171,oUO b.2 12.4 2"!.3 0 14 30 7 1~ ';u 7 13 29 b 15 CO 9 24 • ~ 11-11-7 H 12 31 ;) 1'1 ,7 15 2.9 0 12 .H 2 14 ,7 • 4.H 12,9 ?9,0 1HH,5UlI._ -----_. - --. 11-1~~7_-191,3!j0 tj 1 1 ~2 0 12 31 • t) I1 31 • • 7 .~ 11 •3 31.3 • • • • • • 11-2~-7 9• 7_L9.~ ~_/~O 1 _11.j 1 _~. J2._~_ 4 13. ~.L .---.- .•. __ ..I. __ Q..I.'i._lhL.2. 12- i'.-7 _....J:L.iL . .3 2. ._ . I 11 j:j 195,10U 7 1 1 51 6 1 1 32 4 tI 13 29 • • b.4 11. 1 31.7 209,1)0(1. ____________ 1 1 .B 7 1 1 33 12- 9-7 311,3 .? • U .11 ,2 2 11 ~s j~ 31 ~ 11 )1 • I. l 11 .j~-..l o-l. 2 11 ;)} • • • 10 • .3 29,3 172,940 • • • • H 31• • • • 12-23-7 • • 27 • • • • t:) • • 14b,580 - -- ---- --~--- -----5,5 -- ! ~ 13 c!.9 I 4 ! 2/:'0 0 II 12 3~ .___ J.-,--..JQ- 1_ . • 9.3 2-l.4 b 31 4 7 2b 7 ,) 12 ~ 1 3 1u 3U • • 4.3 ~.q 30,7 14Q,bOO 1- 0-7 • • • 14Q,~CSO b '; 30. b -...I..--~ , 7 .?J - __ .. ____ .___ _.__ .l-_~ 0 c; - . .Jt .J 1. _ . .tLJ._~.~, _ ~Ll.i .. 1·1..~-7 ..l.i.._.3 u 1 l~ l.L.H M 14 31 I 14 .H 7 1 S 2M 7 I l~ 32- iiL .1:1 1~_ a .__ a _.•. ____ 2..a6 .1~J.u.jU. 8 b.~ ".0 .1- . " - J\j __ .A_._ . •... ".A , .. ____ u. __ • _________ u_ ,b , ., . ., ~, .. , .. .. ~.

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