multiple linear regression

Accurate spatial estimation of Precipitation and temperature is very important in hydrological models. Despite the development of automatic meteorological stations in recent years, obtaining reliable climate data in data-deficient areas is still a big challenge. Spatial estimation of climatic data is mainly done by geostatistical methods and satellite images. Nowadays, satellite products are widely accepted in the preparation of climatic maps. These products use satellite images to estimate temperature and rainfall data in points without data, and usually the provided data is accompanied by errors and needs to be recalibrated. It seems that the combination of covariates and satellite products can be effective in increasing the accuracy of climatic maps, especially in areas with complex topography such as Mazandaran province.

In this research, the accuracy of temperature and rainfall products of TRMM satellite was evaluated in Mazandaran province and the possibility of combining them with land features of latitude, longitude and elevation in the form of regression model was investigated. In this regard, the monthly rainfall data of 21 meteorological stations and 48 monthly and 4 annual images of TRMM products in 2014 and 2017 were used. The evaluation indicators are root mean square error (RMSE), mean bias error (MBE), mean absolute percent error (MAPE). Also, the annual temperature and rainfall maps of the province were drawn by satellite products and modified method.

The results showed that the TRMM products have a huge bias error, so that the amount of annual rainfall bias in some years reaches more than 180 mm per year. About the temperature products the underestimation error is more than 2 Celsius degrees. The correlation coefficients of land features and temperature and precipitation data in most of the months provided acceptable results and were significant in 95% confidence level. In general, the relationship between monthly temperature and, latitude and TRMM products was significantly positive in all the investigated months. in the case of altitude, the relationship was negative and strong. But the relationship between temperature and longitude was a little weaker than other covariates. Regarding the precipitation variable, satellite products have a positive and significant relationship in all the investigated months, and the altitude has a negative effect on precipitation data except in the spring months, but the latitude has a positive relationship in the cold months and in the warm months has almost a negative relationship, and no specific seasonal trend was found in the case of longitude. Also, the correlation coefficients of TRMM products with temperature and precipitation data was significant in 100 and 77% of the months, respectively. Investigating the possibility of combining the TRMM products with the latitude, longitude and altitude in a form of regression equation to estimate temperature and precipitation data showed that the hybrid method increased the accuracy of satellite productions, impressively and the error of rainfall and temperature products reduced by about 30% and 70%, respectively. But as expected, the spatial estimation error of precipitation data was higher than temperature in all investigated months. The annual rainfall maps of Mazandaran for the years 2014 and 2017 shows the higher accuracy of the hybrid methods compared to satellite products. So that it shows well the rainy area of the west coastline and also depicts the meridional and altitudinal gradients of precipitation in the Mazandaran province as well. Examining the annual isothermal maps showed that the drawn map with the correction method has a significant difference with the temperature product of the TRMM satellite and has well highlighted the ring of cold areas of Alborz Mountain range and the foothills of Damavand and Alam-Kouh peaks. Also, the modified map has correctly distinguished the temperate coasts of the southern Caspian Sea from the Middle Band and Upper Band regions. In addition, the higher temperature of eastern half of Mazandaran compared to the western half has shown well.

The results of the present research showed that the TRMM temperature and rainfall products alone do not have proper accuracy in the spatial estimation of climate data and have a large bias error, but their combination as a covariate, along with Longitude, latitude and altitude in a regression equation, improved the accuracy of temperature and rainfall maps, and can be used as a new post-processing method in modification of satellite products.

The purpose of this study is to investigate the effects of commercial tourism on the economic, social and physical structures of cities in the Aras Free Zone. The research method of the present study is applied in terms of purpose and comparative in terms of descriptive-analytical and causal methods. In the first part, the mean of each item was calculated using a single sample t-test. Then, according to the feedback of experts, multiple linear regression test was used to analyze the effect of dimensions and test the research hypotheses. The results of this study show that the average of each of the dimensions of commercial (4.35), economic (3.92), social (3.72) and physical (3.31) tourism is higher than the theoretical average (3). Due to the positive difference in the overall average of each dimension, it can be said that business tourism affects the existing structures under study. The results of the correlation test show that between business tourism and the three dimensions of research have all been significant and positive. Multiple linear regression tests also show that there is a strong relationship between the effects of commercial tourism and existing structures (R = 0.99). In total, the three structures were able to predict 0.69% of the variance in commercial tourism (F (9,63) = 35.08 p

This study was conducted with the aim of providing a remotely sensed water quality index in Assaluyeh port using remote sensing technology. so, according to the region conditions, studying of scientific resources and access to satellite data, the parameters of heavy metals, dissolved ions, SST, chlorophyll-a and pH were selected. Then, by reviewing sources, the product MYD091km, MYD021km, MOD021km, MOD091km and level2 images of chlorophyll-a and SST of MODIS sensor were used after preprocessing operations. Also In-situ data were collected Simultaneously with the capture of satellite images in August 2014. Then, the relationships between the water quality parameters and MODIS data, with (R2) from 0.59 to 0.94 and (RMSE) from 0.07 to 0.1 were obtained. Next the images of the MODIS sensor from 2015 to 2017 were prepared and the models were applied to them, then the layers were standardized by fuzzy logic. Also time series of SST data from 2003 to 2017 were prepared and for each month the average pixel values were calculated and based on this, from 2015 to 2017, the variation of this parameter was standardized. Finally, an effective index for assessing the quality of coastal waters was provided by time series of satellite images and the waters of Assaluyeh port were zoned. The results showed that the water quality in 2015 and 2016 has shifted from poor to very poor status in 2017. Based on the results, with the development of a proposed index, in future studies a continuous assessment of environmental monitoring is possible.

Introduction:

Climate change will affect all sectors of the economy to some extent, but the agricultural sector may be the most sensitive and most vulnerable part because agricultural products are highly dependent on climate resources, And according to scientific evidence, future climate change, especially the combined effects of elevated temperatures and elevated atmospheric CO2 concentrations, will have a significant impact on crops (droughts, floods, frosts) on crops( Chiottioud ,1995). The general effects of climate change on crop development vary depending on the plant and study area (Rawlins, 1991), and commenting on the response of different species to climate change requires case studies.

area of study The study area includes west and northwest of the country Uncovering Climate Change in Past Times Climatic data of maximum temperature, minimum temperature, 30-year historical rainfall (1988-2008) were obtained from 23 stations in the west and northwest of the country And Using two nonparametric tests Mann-Kendall and Estimator slop sen, the trend of precipitation and temperature changes was investigated in order to detect climate change phenomenon in the region. Generating climate scenarios in future periods To assess future climate change in the west and northwest of the country, the CCSM4 general circulation model under RCP4.5 scenario is one of a number of new RCP emission scenarios that the Climate Change Intervention Board will develop in its Fifth Assessment Report (AR5) as representative of the linesVarious concentrations of greenhouse gases have been used Predictive model of wheat phenology and yield unctional and phenological data for three years (90-93) with 40 climatic parameters (Table 2) from seven stations (Zanjan, Arak, Sararood, Maragheh, Ghamloo, Ardabil and Orumieh) containing performance and phenology data Was prepared Then, using these data, performance and phenology in the baseline and future period were predicted through simple linear regression, multiple regression. The results consisted of 20 regression models The best model was selected based on R-squard index using RMSE.

February, March, September, and the year are at 99 percent confidence levels, while January, June, July and August are at 95 percent confidence levels. As well as total rainfall, both the upward and downward trends have a significant and decreasing trend at 95% confidence level only in January and March. Changes in temperature and rainfall in the coming period The results of climate change assessment at each of the stations in the future climate show that the mean maximum temperature in the future climate has increased at 14 stations compared to the previous climate and decreased at the other stations. The mean minimum temperature in the future climate has increased in all the stations except for Ghamloo and Sanandaj stations compared to the previous climate. Average temperature also increased at all stations except Ahar, Zarineh, Sarab and Ghomloo stations in all stations compared to past climates Average mean precipitation in all stations excluding sarpolzahab station in future climates It increases with the past climate Impact of Climate Change on Phenology nder the climate change, the length of the flowering stage of the wheat in the future climate will be shorter than in the previous climate, so that the flowering stage length in all the studied stations with the exception of Zarrineh station in the next period (2039-2018 ) Is shorter than the average long-term flowering stage of wheat. he mean flowering stage duration in the basal climate is 136 days, whereas the mean flowering stage duration in the future climate is 118 days, ie the average flowering stage duration in the future climate is 18 days short. Increasingly, the shortening of the flowering stage in future climates is due to the increase in average temperature in May and April and average maximum temperature in December. Impact of Climate Change on PerformanceUnder climate change, wheat grain yields will increase in future climates than in the past, so that at all stations with the exception of Mahabad station, wheat grain yield is higher than the long-term average in the past. verage wheat yield in the past climate was 1863.3 kg / ha but in the future climate it would be 2529.9 kg / ha. Wheat yields are up 35 percent due to the favorable future climate in the region.

tudies show that precipitation in the west and northwest region of the country during the past period has been decreasing and the temperature is increasing in most months of the year. And in the coming period the temperature in all months of the year until the end of 2039 shows an increase of 2.5 to 3.5 ° C. The flowering period is also 136 days for the previous period but 118 days for the next period shortening of flowering stage of wheat plant is due to increase in average temperature in May and April and average maximum temperature in December as well as increase in precipitation in December and February. Comparison of wheat grain yields of the current and past periods showed that wheat grain yields will increase by 35% in the future, due to the increase in average March and April temperatures and average January and March minimum temperatures. It also saw an increase in the average precipitation of February and March in the next period compared to the previous period.

Nowadays, Determining the effective factors on fire is so important, because the plenty areas of forests around the world are destroyed annually by fire and recurrence of that in the long term can irreparably damage to the earth and its inhabitants. It helps us to identify most dangerous locations and times in forest fire. Hence, we can prevent many of driving factors of forest fire by law enforcement, efficient forest management policies and more supervision. In the current study, we identified the effective factors on the fire in Golestan forest through integration of three different methods including multiple linear regression, logistic regression and multivariate adaptive regression spline with Genetic Algorithm.

Golestan Province is in the North of Iran and 18% of it is covered by forests. Golestan Province is a touristic province and several roads pass through its forests and according to statistical records, most of the occurred fires were in proximity of these roads. Our study area is located in 36°53′-37°25′N and 55°5′- 55°50′E and its area is about 3719.5 km2. We selected this area, because includes the most of fires have been occurred in Golestan Province in recent years.

A big fire was occurred on 12 December, 2010 in our study area and we used it as the dependent variable. The actual burnt area and some other data, such as Digital Elevation Model (DEM), the roads network, the rivers, the land uses, and soil types in the area were provided from Golestan Province Department of Natural Resources. Also, geographic coordination of the synoptic weather stations near the area and their data, including maximum, minimum, and mean temperature; total rainfall, as well as maximum wind speed and azimuth in December 2010 were obtained from National Meteorological Organization of Iran.
The land use and soil layers were in scale of 1:100000 and the roads and the rivers layers were in 1:5000 and all of them were provided in 2006. The region DEM is generated from topographic maps of Iran National Cartographic Center in scale of 1:25000 with positional resolution of 30m and we produced the slope and the aspect layers from it in ArcGIS software with the same resolution. The roads and the rivers were in vector format, hence, we used the Euclidean Distance analysis to generate rasters that each cell of them shows the distance from the nearest road or river.
At first we had 5 weather stations, which is very few for GWR. In this regard, we generated 1000 random points in the area and interpolated data to these points using Ordinary Kriging method with exponential semivariogram model in 30m resolution in ArcGIS software.
The multiple linear regression (MLR) model is the generalization of simple linear regression that is modeling the linear relation between one dependent variable and some independent variables. The general formula of MLR is seen below: (1)The unknown coefficients are obtained using least squares adjustment as follows:  (2)The logistic regression (LR) model is a nonlinear model for determination of the relation between a binary dependent variable and some independent variables. If we use the values of 0 and 1 for non-fire and fire points respectively, then the probability that a point be a fire point is obtained by Eq. (3):   (3)If the number of parameters is insignificant compared to the observations, then we use the unconditional maximum likelihood estimation shown by Eq. (4) to compute the unknown coefficients of this model. (4)The multivariate adaptive regression spline (MARS) model is a flexible non-parametric model that requires no assumption about the relation between the dependent andindependent variables. Hence it has a high ability in determination of complex nonlinear relations among the variables. The general formula of MARS is seen below:   (5) is the m’th basic function that is obtained by Eq. (6):  (6)These basic functions are chosen in such a way that leads to minimum RMSE of model.
We use the genetic algorithem (GA) with the fitness function of the normalized RMSE to select the optimum combination of effective factors on forest fire.

In this paper we study the dependence of the forest fire to 14 factors shown in table 1, in the study area. Our results are shown in figures 1 to 3.
 

This research shows that both of the biophysical and anthropogenic factors have significant effects on forest fire in our study area. Just two factors were identified as impressive factors in all three cases including the minimum temperature and the maximum speed of wind. This study concluded to the NRMSE=0.4291 and R2=0.9862 for the multiple linear regression, NRMSE=0.9416 and R2=0.9912 for the logistic regression and NRMSE=0.1757 and R2=0.9886 for the multivariate adaptive regression spline and totally the multivariate adaptive regression spline method showed a better performance in comparison to the other two methods.

Extended Abstract Introduction Electric energy has no storage capacity on a large scale. Considering the importance of this energy in various programs and increasing its consumption in the context of global warming, its future consumption forecast in the energy sector policy will be of significant importance. Therefore, awareness of the variables affecting electricity consumption and the impact of each of them will enable policy makers to make more precise planning and prediction of electricity consumption in the coming years. Therefore, accurate estimation of the amount of consumption with regard to climatic conditions can play an important role in the economic use of electrical energy. The purpose of this research is to investigate the relationship between climatic variables with electricity consumption and prediction of electricity consumption under the influence of climate change in western Iran. Materials and Methods The region studied in this research is western Iran, including provinces of Kermanshah, Kurdistan, Hamedan, Ilam and Lorestan. This region has a variety of climates due to its location on the path of hot and cold air masses and mid-latitude cyclones. The data used in this study are: 1- meteorological data of 13 stations in the region over a 28-year period (1987 to 2014), including minimum temperature, maximum temperature, relative humidity, wind speed, sunshine hours and rainfall, 2- data on monthly electricity consumption during the corresponding period, 3- minimum temperature, maximum temperature and relative humidity data simulated by CCSM4 General Circulation Model. To calculate the heating and cooling requirements, Heating Degree Days (HDD) and Cooling Degree Days (CDD) values were calculated using the minimum and maximum temperature data. First, the relationship between climatic variables and electricity consumption at stations was modeled using multiple regression equations. In the case of significant models based on the data of the CCSM4 model, the electricity consumption at the stations during the period 2080-2080 was estimated under two scenarios RCP4.5 and RCP8.5. Future climate scenarios were then downscaled using the "change factor" method. To verify the downscaled data, the Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Coefficient of Determination (R2) were used. Results and Discussion At all stations, the CDD have a direct and significant relationship with electricity consumption, due to the high consumption of air conditioning/cooling equipment in summer. But the relationship between the HDD and electricity consumption is weaker than the CDD; because in winter, less electricity is used to heat the environment. Especially in warm stations such as Ilam, Dehloran and Sarpole-Zahab, the relationship between the HDD and electricity consumption is not substantially significant. At these stations, during the cold season due to the mildness and shortness of the cold, there is little need for electrical equipment for heating purposes. In contrast, in these three stations, humidity has a significant and inverse relationship with electricity consumption. Other climatic parameters have no significant relationship with electricity consumption. The mean maximum and minimum temperatures in the region in the future period (2021-2080) will increase on average under the RCP4.5 scenario by 1.95ºC and 2.01ºC respectively, and under the RCP8.5 scenario by 3.46ºC and 3.81ºC. Therefore, electricity consumption at all stations in the upcoming period (2021-2080) will increase compared to the past period, and this increase will be much higher in the warm period of the year. The average increase in consumption during the warm period at the stations under the two scenarios will be 80% and 150% respectively. Particularly warm stations in the west of the region, such as Dehloran, Sarpole-Zahab and Ilam in the warm-season months (6 months, from May to October) will experience the highest increase in electricity consumption under two scenarios, of about 110% and 210%, respectively. The lowest increase in demand for electricity in the upcoming period is related to the relatively cold stations of Hamedan, Sanandaj, Saqez and Bijar. Because of the mountainous nature, the high altitude and the longer cold period, the main need of these stations is heating, a significant part of which is supplied by natural gas. This clearly has little dependence on electricity. But in any case during the warm period of these stations, which is shorter, and lasts for 4 months (June to September), the increase in consumption is lower than in warm stations and under the two scenarios, would be about 60% And 110%, respectively. Other stations like Khorramabad, Kermanshah, Kangavar, Boroujerd and Islamabad will have an intermediate level of consumption. However, it should be noted that regardless of the increase, electricity supply for larger and more populous cities such as Kermanshah and Hamedan will be more important than warm cities. There is not much increase in consumption in cold-period months at any warm and cold station. Conclusion Since a significant part of the electricity consumption in the region is due to the use of conditioning/cooling equipment, any change in temperature during the warm period will be effective in increasing or decreasing the use of those equipment, and consequently, increasing power consumption. Considering the significant increase in the temperature of the region during the 2021-2080 period under the two scenarios used, it is necessary to take appropriate strategies to deal with the drastic increase in electricity consumption in the future, especially during the warm period of the year.

Forest areas are among the most important natural and ecological resources on the Earth and are considered as one of the main pillars of sustainable development in any country. Fires ruins almost 5500 hectares of Iran’s forests yearly. In this research, firstly, the fire points were identified using the fire data of Forest Organization in combination with MODIS sensor data between 2012 and 2017. Due to the fact that more than 75% of fires were happened in the hot season of the year (June, July, and August), the data of the three months was used for modeling. Then, the effective parameters in fire occurring were evaluated and the dependent parameters were removed. Accordingly, two methods, including multiple linear regression and multivariate adaptive regression spline were studied to predict the fire risk. Some important parameters including the root-mean-square error (RMSE), R2, the correct estimation percentage of fire and non-fire points, and error distribution were used to evaluate. After modeling, it was found that the multivariate adaptive regression spline has better performance—where its RMSE of test data was 0.1628, its R2 of test data was 0.893, and its correct estimation percentage of test fire points and test non-fire points was near 94% and 88% respectively, as well as its error distribution was better than the other method. This actually shows that modeling with a local method is very better than modeling with a global method. Therefore, the risk map resulted by multivariate adaptive regression spline has better reliability compared to those of the other method. Finally, the high-risk areas were recognized using the risk map of this method. The traits of these areas were a short distance to residential areas and roads, having rich soil with organic materials, relatively high temperature, and low height.
 

In 2000, a convention was established in the United Nations to improve the quality of human life in which the principles of the Millennium Development Goals were adopted. One of these goals was to ensure the stability of the environment and natural resources. In the contemporary world, the value of forests is about 120 billion dollars and the livelihood of almost 9.1 people is dependent on forest (in)directly.
According to the opinion of global experts including FAO, if the forest cover of a country is less than 25% of that country’s area, that country is in critical condition in terms of the human environment. Almost 190000 hectares of Iranian forests have been ruined by fire in a 28-year period. Forest fire not only changes the natural ecosystem and ruins many plant and animal species of a region, but also makes other destructive effects like air pollution, respiratory problems, soil erosion, increased flowing surface waters, increased acidity of soil, decreased fertility, tourism industry losses, manufacturing industry and economy losses, and even climate change.
Immediate and accurate detection of the fire location and the ability to determine the effective parameters on it, as well as the detection of the areas with high-risk of fire is among the main concerns of environmental protection and disaster management. We can prevent the fire by training people, making effective regulations and management policies, and increased monitoring to deal with fire triggers. Moreover, in the case of fire occurrence, we must take necessary actions like deploying fire-fighting equipment near hazardous areas and making easy access to these areas. In fact, nowadays, the increasing importance of protecting the forests and natural resources has led to change the focus from crisis management to risk management.

The modeling was not possible without non-fire points. Accordingly, at the beginning, some points are randomly selected in the whole area with a certain distance from the fire points and are identified as non-fire points. To implement the methods in MATLAB programming environment, firstly, the parameters used in the modeling are extracted using the maps of these parameters for fire and non-fire points. These parameters are used as inputs in each of these methods. 
Constantly, 70% of the selected data were used as the training data and 30% of them were used as the test data. Initially, the multivariate linear regression and then the multivariate adaptive regression spline were used for modeling. The steps of the research implementation are shown in Figure (1).
After implementation of the modeling, the evaluation parameters of each method were provided to compare. Then, the risk map of the area was provided using trial points and Inverse Distance Weighting (IDW) and by employing 12 lateral points for each method (Figures 2 and 3). The points with a high risk were extracted from the resulted map. Then, the main traits of these points are considered as the traits of high-risk points.
 
Fig. 1. The steps of the research implementation

Fig. 2. Fire risk map provided using the MLR method on test data

Fig. 3. Fire risk map provided using the MARS method on test data

 
After removing the dependent parameters from the effective parameters on the fire, the optimal effective parameters are presented in Table (1). These parameters are divided into three groups including climate, ground physical, and human parameters.
The modeling of fire risk was done by two methods. In the training and testing data section, the RMSE and R2 are presented in Table (2) for multivariate adaptive regression spline and multivariate linear regression methods, respectively. The results achieved by the training data section indicate that the training procedure is more accurate (R2 closer to 1) and with less error (less RMSE) in the multivariate adaptive regression spline than those achieved by the multivariate linear regression method. The appropriate amount of evaluation parameters for test data shows that the model does not experience over-fitting in these methods.
Table 1. Effective parameters on fire occurrence in the case-study area

In the linear regression method, the two parameters of the correct estimation percentage of fire points and non-fire points have a low value, hence, the worst possible scenario has happened and the risk map has the least amount of reliability. In the multivariate adaptive regression spline, the fire and non-fire points are simultaneously estimated with a high accuracy. This makes the risk map provided by the multivariate adaptive regression method becomes to be more reliable.
As seen in the results, the risk map provided by the multivariate adaptive regression spline method has a very higher reliability compared to the risk map provided by multivariate linear regression method. Hence, the risk map resulted by the first method was used to determine the features of the areas with a high risk of fire (Figure 4).
Since the fire risk has a normal distribution, the areas which satisfy Equation (1) are among the 2.5% of the areas that have the most fire risk.
(1)
where  is the average,  is the standard deviation, and R is the fire risk. The main features of the mentioned areas can be used as the important tools for decision making. The extraction of high-risk areas is done in ArcGIS environment. Statistical analysis of effective parameters’ features in these areas shows some key points. These features include low distance from the residential regions (less than 2 km), low distance from the road (less than 2 km), having mollisol, relatively high average temperature (more than , and low height (less than 50 m).

Fig. 4. High risk map provided using the MARS method on test data

This research attempted to identify the optimal method for modeling of fire points risk using climate, ground physical, and human parameters. Therefore, an accurate local method (MARS) was used along with a non-local method (MLR).
In the test data and the training data sections, the MARS method had the lowest RMSE and a value closer to 1. The outputs showed that the MARS method had a more accurate performance in the estimation of the fire and non-fire points compared to the MLR method. This indicated the high reliability of the MARS method. After determining the optimal method for the modeling of the area’s fire occurrence, the points of the area with high risk of fire were detected. After doing a statistical analysis it was found that these points have some fundamental features including low distance from the residential regions (less than 2 km), low distance from the road (less than 2 km), having mollisol, relatively high average temperature (more than  and low height (less than 50 m).