Least Squares Regression with an Explanatory Variable

2 Least Squares Regression with an Explanatory Variable 

Regression analysis in time series analysis is a very useful technique if an explanatory variable is available. Explanatory variables may be any variables with a deterministic relationship to the time series. VAN STRATEN and KOUWENHOVEN [1991] describe the dependence of dissolved oxygen on solar radiation, photosynthesis, and the respiration rate of a lake and make predictions about the oxygen concentration. STOCK [1981] uses the temperature, biological oxygen demand, and the ammonia concentration to describe the oxygen content in the river Rhine. A trend analysis of ozone data was demonstrated by TIAO et al. [1986]. 

In the time series example it is fortunate that the nitrate concentration of the feeder stream in the storage reservoir system is known. Now we have to test if this parameter can explain the nitrate concentration in the storage reservoir. Approximately 70% of the total amount of water which is flowing into the storage reservoir system was measured as originating from the feeder stream from the Lawitz gauge. 

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