multiple regression

Soil erosion is one of the most important and serious threats to food security and as a consequence of human life. In order to perform soil protection activities against soil erosion, knowledge about the amount of soil loss tolerable is very important. In fact, the soil loss tolerable is the potential for soil erosion, loss of productivity and lost production, and the final criterion for controlling soil erosion and degradation of land. Soil thickness methods, particularly Skidmore equation, based on their ability to estimate the tolerable amount of soil loss have been widely used. In the mathematical function developed by Skidmore based on soil thickness, the soil loss tolerable is calculated based on the soil's current depth, the lowest and maximum soil depth for sustained growth of crops, and the upper limit of tolerable erosion in accordance with the environment. Since the determination of soil loss tolerance by soil thickness method and the Skidmore equation requires time, cost and energy, the researchers have tried to estimate the soil tolerance is supported by regression methods using pedotransfer functions and easily available soil properties. Therefore, the present study was carried out with the aims of determining the tolerable tolerance of soil loss by thickness method and the development of regression pedotransfer functions for estimating this property in the upstream of the dam.

The study is place on Kamfiruz Watershed with an area of 422 km2, an average annual precipitation of 443 mm and an average annual temperature of 14 °C. It is closed to the Dorudzan Dam sub-basins and is considered as one of the five parts of Marvdasht plain in Fars province. For this work, 60 soil profiles were excavated by excavating machine. In addition to measuring the depth of soil, some physico-chemical soil properties were measured from the surface layer (0-30 cm) including; soil texture, organic matter, salinity, percentage calcium carbonate, mean weight diameter in the laboratory and filed. In order to develop regression models for estimating the tolerable soil loss, information from 60 soil profiles was divided into two data-sets. One set of the data with 42 samples (70% of whole samples) was used for developing the models and another set of the data with 18 soil samples (30% of whole samples) was used for validation. Multiple linear regression was used to develop the linear models. The same soil properties used in the multiple regression method were considered as inputs in the tree regression method to estimate the tolerable amount of loss.

The results showed that the minimum and maximum Z1 parameters (the lowest soil depth for stable growth of crops in the study area) were considered as 0.25 and 0.51 m based on the current depth of soil. Organic matter of the soils with the highest standardized coefficient (Beta = 0.44) and the highest correlation (-0.77) with soil loss tolerance was the most important soil properties for estimating the soil loss tolerance. In the regression model, only the coefficients of four characteristics of permeability, soil aggregate stability, pH and organic matter appeared among the soil grazing characteristics and entered into the model. Based on the evaluation statistic, tree regression method with the highest determination coefficient in both calibration data sets (R2 = 0.96) and validation (R2 = 0.78) and the lowest error value in the validation data (RMSE= 0.29 ton ha-1 year-1) and validation (RMSE = 0.125 ton ha-1 year-1) were more efficient than the multiple regression method in estimating the tolerable soil loss.

Soil loss tolerance was estimated using regression methods (multiple linear regression and regression tree) in Doroudzan Watershed, Fars province. The soil loss tolerable determined using Skidmore method, was 1.04 tons per hectare per year ranging from 0.29 to 2.25 ton ha-1 year-1. The soils of this area are slightly deep and their depth varies from 0.4 m in the marginal areas in the upstream parts of the catchment area of the dam and the slope of mountain up to 2 meters in the center of the plain with agricultural lands uses. In general, the tree regression method had a better performance than linear regression method for estimating the soil loss tolerance based on the statistical indices.

Monitoring and management of saline soils depends on exact and updatable measurements of soil electrical conductivity. Large scale direct measurements are not only expensive but also time consuming. Therefore application of near ground surface sensors could be considered as acceptable time- and cost-saving methods with high accuracy in soil salinity detection. . One of these relatively innovative methods is electromagnetic induction technique. Apparent soil electrical conductivity measurement by electromagnetic induction technique is affected by several key properties of soils including soil moisture and clay content.
Soil salinity and apparent soil electrical conductivity data of two years of 50000 ha area in Sabzevar- Davarzan plain were used to evaluate the sensitivity of electromagnetic induction to soil moisture and clay content. Locations of the sampling points were determined by the Latin Hypercube Sampling strategy, based on 100 sampling points were selected for the first year and 25 sampling points for the second year. Regarding to difficulties in finding and sampling the points 97 sampling points were found in the area for the first year out of which 82 points were sampled down to 90 cm depth in 30 cm intervals and all of them were measured with electromagnetic induction device at horizontal orientation. The first year data were used for training the model which included 82 points measurement of bulk conductivity and laboratory determination of electrical conductivity of saturated extract, soil texture and moisture content in soil samples. On the other hand, the second year data which were used for testing the model integrated by 25 sampling points and 9 bulk conductivity measurements around each point. Electrical conductivity of saturated extract was just measured as the only parameter in the laboratory for the second year samples.
Results of the first year showed a significant correlation between electrical conductivity and apparent conductivity with a regression coefficient of 0.78. Although multiple linear regression by inclusion of soil moisture and clay content as independent variables improved the regression coefficient to 0.80 but the effect of clay content was not significant in this multiple model. Sensitivity analysis by maintaining one variable at its average value and changing the second variable also showed greater sensitivity of the model to soil moisture in comparison with soil clay content. Generally under estimation of soil moisture and over estimation of soil clay content produced about 63 to 65 percent Mean Bias Error (MBE) while over estimation of soil moisture and under estimation of soil clay content produced about 35- 37 percent of MBE. So the model is quite sensitive to both parameters and they cannot be estimated in the field by feeling and the other field methods. Simple linear regression model between ECe and EMh was tested on the second year because the errors in estimating soil moisture could be imposed a significant error on estimating soil salinity. Once the model was tested for estimation of soil salinity in the central point based on EMh reading at the center and then it was tested for estimation of soil salinity based on the average EMh of 9 points in each location. Results showed that the correlation between soil salinity and apparent soil electrical conductivity could be improved to 0.98 using the average of 9 measurements instead of 1 measurement.
Based on the results the electromagnetic induction device is sensitive to soil moisture. Although its sensitivity to clay content is less than the sensitivity to moisture content, but the total model error as a result of over estimating soil moisture is about equal to its error resulted from under estimating clay content and vice versa. So the field and feeling methods could not be implemented as inputs for the multiple regression models but these methods have enough accuracy to divide soil samples into two groups of dry and wet soils or sandy or clayey soils, on the other hand measurements of these parameters imposes more cost and time to soil salinity surveys. Results also showed that the repeated EM measurements around each sampling point could improve the strength of the regression. Therefore regarding to the sensitivity of the technique to soil moisture three methods are suggested to improve accuracy of calibration: a)- measurement and calibration under the same moisture conditions; b)- field approximation of soil moisture and dividing soil samples into two groups of dry and moist soils and deriving two different groups of calibration equations.

Side weirs are used in drainage systems, flood control, runoff collecting and many water resources and environmental projects. In this study, discharge coefficient in trapezoidal sharp crested side weirs was investigated by designing 18 weirs in subcritical condition and the effective factors on this parameter were studied. Some equations presented for calculating discharge coefficient with 4.3 and 5.4 percent error by using statistical methods and multiple regression. Results demonstrate that considering the side slope of the weir as an effective factor on discharge coefficient, increase accuracy of computations 1.2 up to 2.3 percent. Also, according to the calculations, the most important factor on discharge coefficient in this type of weirs is the ratio of overflow length to the length of the weir and omitting this factor leads to increase the error up to 1.4 percent.Side weirs are used in drainage systems, flood control, runoff collecting and many water resources and environmental projects. In this study, discharge coefficient in trapezoidal sharp crested side weirs was investigated by designing 18 weirs in subcritical condition and the effective factors on this parameter were studied. Some equations presented for calculating discharge coefficient with 4.3 and 5.4 percent error by using statistical methods and multiple regression. Results demonstrate that considering the side slope of the weir as an effective factor on discharge coefficient, increase accuracy of computations 1.2 up to 2.3 percent. Also, according to the calculations, the most important factor on discharge coefficient in this type of weirs is the ratio of overflow length to the length of the weir and omitting this factor leads to increase the error up to 1.4 percent.

Hydrologic drought which usually affects wide regions can be studied through Low flow index. In this study, to predict hydrologic drought in North Karoon watershed, 14 stations with suitable and long enough duration data were recorded in the 1387-88 water year. Then 13 physiographic and climatic characteristics of the chosen stations were used to perform homogeneity test for cluster analysis. 7 day low flow series were calculated in each station and according to chi-square and Kolomogragh smirnov tests and parameter, 2 parameter gamma distribution was selected as the best regional distribution for this region. Therefore, a seven day low flow index was estimated using FREQ for 5, 10, 20, 50, 100 return periods. Regional analysis was performed using a multiple regression method. Moreover, flow duration curves were delineated to obtain Q95 index. Then, zoning maps for Q95، Q7, 2، Q7, 10, Q7, 100 were prepared. The results of regional analysis indicated that the averages of height and slope were the two most effective parameters in low flow in this watershed. The investigation of zoning maps showed that southeastern part of this watershed experiences severe droughts compared with other parts.

Because of the scarcity of in situ measurements، estimation of soil temperature by other means is very indispensable، as for Irrigation management and scheduling when in different field conditions. So far، many regression models have been developed for an estimation of soil temperature، using meteorological data under bare soil. Throughout this study، the performance of COUP simulation model and multiple regression approach for an estimation of soil temperature within an experimental plot، and under grass (Lolium perenne) canopy (in Karaj climatic conditions has been evaluated. Soil physical parameters، estimated as based on soil analysis (soil texture، bulk density)، and daily meteorological data (including maximum and minimum temperature، wind speed، pan evaporation، sunshine hours and rainfall) as well as vegetation data (crop height، root depth and Leaf Area Index (LAI) were made use of to run the model over the growing period. Soil temperature was measured using standard soil thermometers at depths of 10، 30، 50 and 70 centimeters. Stepwise approach was employed to develop suitable regression models. Following a running of both simulation and statistical models، the observed and simulated data values were compared، making use of statistical indices. The results revealed that، by inclusion of variables affecting incoming radiation i. e. crop height، and leaf area index، the accuracy in the prediction of soil moisture increases.

Reference evapotranspiration (ETo) is an essential parameter required for proper management of agricultural crop irrigation. ETo is influenced by many different hydrological variables and as a result is a very complex procces. ETo is usually estimated by empirical or process-orinented models (mathematical relationships) from historical weather data. The need for accurate estimates of ETo and the complexity of developing models to describe such complex process magnifies the need for developing new data mining methods. In this paper, the possibility of using a combined method of multiple linear regressions with principal componenets analysis (MLR-PCA) for estimating reference evapotranaspiration was investigated. In this analysis, measured daily meteorological data of Kerman synoptic weather station recorded from 1996 to 2005 were used. Three principal componenets that explained 80% of the total variance of the data were recognized as the principle componenets and others as disorder. Using the extracted principle componenets, a multiple linear regression model was developed to estimate ETo. The statistic index of t for assessing the results of a fixed constant and each componenets of PC1 and PC2 were determined. According to the results, all coefficients were significant at the level of 95% and PC1 had more importance than the other component namely PC2. This revealed that the variables of radiation intensity, relative humidity, sunshine hours, minimum temperature and maximum temperature had more importance in estimating reference evapotranspiration than other climatological parameters. Comparison of MLR-PCA model with Penman-Monteith results showed that about 82% of the total amount of the ETo variance is defined by the three aformenstioned principle componenets.

This study was down in Forest Park of Noor. In order to determination of tree ring response to climatic variations, 35 cores were taken from dominant natural stand of common ash (Fraxinus excelsior L.). The guide of this study was finding which climatic variables are effective in the ring width growth of ash in current growing year and previous years (one, two and three years before current growing year) by multiple regression models at the North of IR-Iran. Totally, 85 annually, monthly seasons and seasonal growth climatic variations of precipitation, temperature, heat index, evapotranspiration and water balance were analyzed. The best multiple regression models were explained 83 percent of total variance of the growth of common ash. The results show that the growth of common ash was related to the previous year's climatic variations than that of the current year. The most effective role of climatic variations was due to the first and second preceding years (55%). Evapotranspiration of July and September, and precipitation of May in the second and precipitation of March in the third previous years, all were positively affected the growth of this species. This study revealed that ash is interested in warmer condition on early and middle of seasonal growth in present of available humid, and precipitation in the months of early growing season (Ordibehesht-Khordad of two previous years).

Since the fluctuations of the Persian Gulf Sea Surface Temperature (PGSST) have a significant effect on the winter precipitation and water resources and agricultural productions of the south western parts of Iran, the possibility of the Winter SST prediction was evaluated by multiple regression model. The time series of PGSSTs for all seasons, during 1947-1992, were considered as predictors, and the time series of MSSTs during 1948-1993, as the prrdictand. For the purpose of data reduction and principal components extraction, the principal components analysis was applied. Just the scores of the first four PCs (PC1 to PC4) that accounted for the total variance in predictor field were considered as the input file for the regression analysis. For finding the dependency of each principal component to the first time series of the PGSST, the Varimax rotation analysis was applied. The results have indicated that PC1 to PC4 respectively are the indicator of temperature changes during winter, autumn, Spring and Summer. According to the regression model, the components of PC1, PC2 and PC4 were significant at 5% level. But the components of PC3 was insignificant. The results indicated that the significant variables are held accountable for the 33.5% of the total variance in the winter PGSSTs. It became obvious that for the prediction of the winter PGSST, the PGSST during the winter of the last year has a particular importance. At the next stage, autumn and summer temperature have also a role in prediction of winter PGSST.

Elm leaf beetle were reared under controlled conditions (25± 2 oC, 70± 5%R.H. and 16L: 8D) to determine relationship between biological traits and the number of eggs per female on different hosts and to evaluate correlation between traits. U. carpinifolia, U .c. var. umbraculifera, U. glabra var. pendula and Celtis caucasica were examined as hosts. The biological traits consisted of 1st, 2nd and 3rd larval developmental times first, second, and third larval percent mortality rates prepupal and pupal developmental times male and female longevity and pre-ovipositional period recorded during experiments. The relationships between traits and the number of eggs per female were determined by multiple regression (Foreward selection and stepwise). The correlation between traits was evaluated, too. The results showed that the number of eggs per female were mostly affected by certain special traits such as 2nd and 3rd larval developmental time, pre-ovipositional period and male longevity which are distinct in different hosts and seasons.

An approach for regional low flow frequency analysis is to use multiple regression techniques for obtaining relationships between low flows with specific return periods and catchments characteristics. In this paper, this method has been used. After single-site frequency analysis for 20 stream gauging stations, homogeneity test was performed. Regional relationships between low flows with return periods 2 , 5 , 10, and 20 years and catchments characteristics were derived. For this purpose, catchment area, mean elevation, minimum elevation, shape factor, main channel length, length of main chanel from catchment centroid to outlet, forest area, mean annual rainfall, and mean catchment slope as model inputs were examined and cachment area, mean elevation, and mean catchment slope entered to the models. Finally, the mean relative error of models for different return period, 2, 5, 10, and 20 years, was computed 41.1, 41.3, 45.0, 47.2 percent, respectively that in comparison with other studies, it displays smaller errors.