农业工程学报
農業工程學報
농업공정학보
2013年
11期
1-10
,共10页
曲线拟合%数学模型%误差%最小一乘法%生产函数%平均绝对误差%平均绝对百分误差%粮食产量
麯線擬閤%數學模型%誤差%最小一乘法%生產函數%平均絕對誤差%平均絕對百分誤差%糧食產量
곡선의합%수학모형%오차%최소일승법%생산함수%평균절대오차%평균절대백분오차%양식산량
curve fitting%mathematical models%errors%least absolute deviation(LAD) method%production function model%Mae(mean absolute error)%Mape(mean absolute percentage error)%grain products
该文提出了中国粮食产量与影响粮食产量的一些主要因素之间,更多呈现的是指数关系,也少量呈现幂指数关系,为了获得较小的误差从而有较准确的描述定义了一种新的指数型生产函数;指出了最小一乘法是一种能找到在数据背后隐含的,对数据起支配控制作用的“隐函数”的最好方法.将二者捏合起来,用最小一乘法对指数型生产函数模型进行拟合,可以找到符合中国粮食变化的某些规律.该文介绍了最小一乘法和指数型生产函数,将影响粮食产量的5个主要因素(化肥施用量、粮食播种面积、成灾面积、农业机械总动力、第一产业就业人数)与中国粮食产量建立关联,用最小一乘法对生产函数模型进行拟合,并对中国1983-2011年的数据进行处理.在获得29 a间中国粮食产量的Mae(平均绝对误差)不超过393万t,以及Mape(平均绝对百分误差)小于0.87%的数据处理结果的基础上,对数据给出的结论进行了解释和分析.1983-2011年的29 a间,中国粮食产量的增长主要取决于化肥施用量和农业机械总动力,其中化肥施用量还继续在起“正”影响,而农业机械总动力趋于动态饱和,属于理论上的“负”影响,但不构成实际的“负”效应;粮食播种面积是最大的“正”影响,粮食产量在粮食播种面积在不增条件下,依然可以增长,但是增大粮食播种面积将能够迅速提高中国的粮食产量;成灾面积是粮食增长的“负”影响,影响的绝对量值在增加但相对量值在减小;由于受1984-1991年第一产业就业人数急剧增长的巨大冲击及滞后效应影响,第一产业就业人数的减少对粮食增长构成“负”影响,随着农业现代化与城镇化进程的发展,这种“负”影响在不断减小中.文中对上述这些定性结论给出了具体的定量值.该文并对2012年粮食产量进行了预测,其值为59133万t,预测的误差为0.3%;也对2013年粮食产量进行了预测,其值为61148万 t.该文最后对最小一乘法、指数型生产函数等存在的问题进行了必要的讨论.最小一乘准则意义下的指数型生产函数,对中国粮食产量与主要影响因素之间关系的描述具有一定的准确性和指导意义.
該文提齣瞭中國糧食產量與影響糧食產量的一些主要因素之間,更多呈現的是指數關繫,也少量呈現冪指數關繫,為瞭穫得較小的誤差從而有較準確的描述定義瞭一種新的指數型生產函數;指齣瞭最小一乘法是一種能找到在數據揹後隱含的,對數據起支配控製作用的“隱函數”的最好方法.將二者捏閤起來,用最小一乘法對指數型生產函數模型進行擬閤,可以找到符閤中國糧食變化的某些規律.該文介紹瞭最小一乘法和指數型生產函數,將影響糧食產量的5箇主要因素(化肥施用量、糧食播種麵積、成災麵積、農業機械總動力、第一產業就業人數)與中國糧食產量建立關聯,用最小一乘法對生產函數模型進行擬閤,併對中國1983-2011年的數據進行處理.在穫得29 a間中國糧食產量的Mae(平均絕對誤差)不超過393萬t,以及Mape(平均絕對百分誤差)小于0.87%的數據處理結果的基礎上,對數據給齣的結論進行瞭解釋和分析.1983-2011年的29 a間,中國糧食產量的增長主要取決于化肥施用量和農業機械總動力,其中化肥施用量還繼續在起“正”影響,而農業機械總動力趨于動態飽和,屬于理論上的“負”影響,但不構成實際的“負”效應;糧食播種麵積是最大的“正”影響,糧食產量在糧食播種麵積在不增條件下,依然可以增長,但是增大糧食播種麵積將能夠迅速提高中國的糧食產量;成災麵積是糧食增長的“負”影響,影響的絕對量值在增加但相對量值在減小;由于受1984-1991年第一產業就業人數急劇增長的巨大遲擊及滯後效應影響,第一產業就業人數的減少對糧食增長構成“負”影響,隨著農業現代化與城鎮化進程的髮展,這種“負”影響在不斷減小中.文中對上述這些定性結論給齣瞭具體的定量值.該文併對2012年糧食產量進行瞭預測,其值為59133萬t,預測的誤差為0.3%;也對2013年糧食產量進行瞭預測,其值為61148萬 t.該文最後對最小一乘法、指數型生產函數等存在的問題進行瞭必要的討論.最小一乘準則意義下的指數型生產函數,對中國糧食產量與主要影響因素之間關繫的描述具有一定的準確性和指導意義.
해문제출료중국양식산량여영향양식산량적일사주요인소지간,경다정현적시지수관계,야소량정현멱지수관계,위료획득교소적오차종이유교준학적묘술정의료일충신적지수형생산함수;지출료최소일승법시일충능조도재수거배후은함적,대수거기지배공제작용적“은함수”적최호방법.장이자날합기래,용최소일승법대지수형생산함수모형진행의합,가이조도부합중국양식변화적모사규률.해문개소료최소일승법화지수형생산함수,장영향양식산량적5개주요인소(화비시용량、양식파충면적、성재면적、농업궤계총동력、제일산업취업인수)여중국양식산량건립관련,용최소일승법대생산함수모형진행의합,병대중국1983-2011년적수거진행처리.재획득29 a간중국양식산량적Mae(평균절대오차)불초과393만t,이급Mape(평균절대백분오차)소우0.87%적수거처리결과적기출상,대수거급출적결론진행료해석화분석.1983-2011년적29 a간,중국양식산량적증장주요취결우화비시용량화농업궤계총동력,기중화비시용량환계속재기“정”영향,이농업궤계총동력추우동태포화,속우이론상적“부”영향,단불구성실제적“부”효응;양식파충면적시최대적“정”영향,양식산량재양식파충면적재불증조건하,의연가이증장,단시증대양식파충면적장능구신속제고중국적양식산량;성재면적시양식증장적“부”영향,영향적절대량치재증가단상대량치재감소;유우수1984-1991년제일산업취업인수급극증장적거대충격급체후효응영향,제일산업취업인수적감소대양식증장구성“부”영향,수착농업현대화여성진화진정적발전,저충“부”영향재불단감소중.문중대상술저사정성결론급출료구체적정량치.해문병대2012년양식산량진행료예측,기치위59133만t,예측적오차위0.3%;야대2013년양식산량진행료예측,기치위61148만 t.해문최후대최소일승법、지수형생산함수등존재적문제진행료필요적토론.최소일승준칙의의하적지수형생산함수,대중국양식산량여주요영향인소지간관계적묘술구유일정적준학성화지도의의.
The relations between China’s grain yield and some main factors influencing the grain yield, more present the exponential function and few exponent sign function relations. To describe with a new type of exponential production function can obtain a better result because of less error. The paper pointed out that the least absolute deviations (LAD) method, as its excellent properties, may be a best method to find the“implicit function”which is behind the data and control the data. To knead the two together, with the LAD method to fit the exponential production function, trying to find out some rules for China's grain change is a subject that is worth of exploring in theory and application. The paper introduces the LAD method and the exponential production function, establishes correlations between the China’s grain yield and its 5 major influencing factors (consumption of chemical fertilizer, total sown area, total area affected by natural disaster, total agricultural machinery power, and total employed persons of primary industry). The production function model was fit with the LAD method, and the data of 1983-2011 were calculated. The results with Mae (mean absolute error) not over 3.93 million tons and Mape (mean absolute percentage error) not more than 0.87%for China’s grain yield during the 29 years were obtained, and the conclusions were explained and analyzed;The analysis showed that, in the 29 years of 1983-2011, the growth of China’s nation grain yield mainly depended on the consumption of chemical fertilizer and the total agricultural machinery power, of which the consumption of chemical fertilizer is still playing a positive roll up to now, while the total agricultural machinery power is dynamically in a saturated state. Theoretically it should have a “negative”effect now, but in reality it does not. The total sown area was the most influencing“positive”factor. The national grain yield may still grow further without increasing the total sown area, but increasing the sown area can rapidly boost the China’s nation grain yield. The total area affected by natural disaster imposed “negative” effect on the growth;However, the trend of its influence is increasing in terms of absolute values, but is decreasing in terms of relative values. By the huge impact and lagged effects of the rapid growing of the total employed population of primary industry in China during 1983-1993 period, the reduction of the total employed population of primary industry to grain growth constituted “negative” impact. With the modernization of agriculture and urbanization development, this “negative” impact continued to reduce. These conclusions give the specific quantitative values. The paper predictes that the grain yield for year 2012 is 5.9133 10× t, the later result indicates the absolute error is 8 1.78 10× t, and the relative error is 0.3%. For year 2013, the prediction is 6 6.1148 10× t. In the last the paper gives 8 some discussion about the LAD method, the exponential production functions and so on, and is concluded that the exponential production function under the meaning of LAD criterion to describe the relationships between China's grain yield and the main effect factors, has a certain accuracy and guiding sense.
