nonlinear regression

The city of Arak is one of the industrial centers of the country that has been facing population growth in recent decades. Increasing population as well as increasing energy consumption on the one hand and global warming on the other hand have caused changes in climatic elements such as relative humidity. In this paper, the relative humidity behavior of Arak city during the period 1961 to 2017 was investigated using Mann-Kendall statistical test and linear and nonlinear regression. The findings of this study showed that the trend of relative humidity of Arak station is different at different hours during the year and seasons. The most significant changes in the relative humidity of Arak are related to 6.5 and 9.5 hours, which has a downward trend. Using SDSM statistical downscaling model, relative humidity statistics of Arak until 2070 were predicted. The findings of this part of the study showed that the SDSM model can simulate and predict relative humidity. According to two scenarios A2 and B2, the relative humidity of Arak will decrease in the future

The length of data is very important in forecast and analysis of annual temperature. The long term data may have fluctuations. The time series of temperature as a trend, can show seasonality and cyclical changes and will appear better and frequency analysis result could be improved. Maximum Statistical period of temperatures data in the stations of Iran is about 60 years that is a short-term. Mashhad has 127 years long-term monthly temperatures (2011-1885). The recent 60 years (2011-1951) have been observed by The Mashhad Synoptic Station and the remaining 67 years (1940-1885) observed by the America's consulate which was located in Mashhad. These 127-years long-term data have missing values that should be repaired. There are some stations that have long-term temperatures data and have a good correlation with temperatures of Mashhad. This station consists of Jask (Iran, founded in 1893), Serakhs and Kyzyl (Turkmenistan, founded in 1900 and 1893 respectively), Turkestan (Kazakhstan, founded in 1885) and Baghdad (Iraq, founded 1893).
Mashhad a city in the center of Khorasan Razavi Province, is located in the northeast part of Iran at a latitude of , longitude of and an altitude of 946 MSL. Mashhad has 127 years long-term monthly temperatures (2011-1885). The recent 60 years (2011-1951) have been observed by The Mashhad Synoptic Station and the remaining 67 years (1940-1885) by the America's embassy which has been located in Mashhad observed.
In linear regression, the model specification is that the dependent variable, is a linear combination of the parameters (but need not be linear in the independent variables). For example, in simple linear regression for modeling n data points there is one independent variable: , and two parameters, and : according to equation (1).
In multiple linear regressions, there are several independent variables or functions of independent variables, according to equation (2).
Multiple linear and nonlinear patterns were used for estimating missing data in this paper. Three Linear models finally accepted and were used for this purpose.
Multiple linear models for restoration of data in years 1904-1895, 1949-1941, January, February and July 1905, December 1910, January and February 1914, January 1913, May 1932, September to December 1933 and February and March 1937, by two base stations: Jask and Turkestan, according to equation (3). Univariate linear pattern according to equation (4) using data from the years 1885-1890 by using Turkistan stations to extending data and reconstruction of June, July and August 1892, October 1894 and March 1951 were used.
(4) Univariate linear pattern by using the temperature of Jask station to reconstruct July 1918 to December 1919 were used. This pattern is according to equation (5).
The coefficients of determination of these models are 0.98, 0.96 and 0.93 respectively. Classical tests and diagnostic of models showed acceptance of them. F-statistics of these models are 23160, 31080 and 14480, respectively. The P-value for all tests is closed to zero. VIF for all models are less than 10. Durbin-Watson statistic located in accepted regions.
Multiple linear and nonlinear models were used for estimating missing data in this paper. Three Linear models finally accepted and were used for this purpose. The coefficients of determination of these models are 0.98, 0.96 and 0.93 respectively. Classical tests and diagnostic of models showed acceptance of them. F-statistics of these models are 23160, 31080 and 14480, respectively. The P-value for all tests is closed to zero. VIF for all models are less than 10. Durbin-Watson statistic located in accepted regions .Therefore 127 years of monthly temperature for Mashhad (1885 to 2011) was completed. The test of homogeneity, independence, randomness and outliers were done and accepted. The analyzing of 127 Mashhad annual temperatures showed that there is a change point and an increasing trend from 1986.