Theoretically, smoothing techniques are designed to diminish irregular fluctuations or oscillations in time series data. That explicitly implies the techniques assume smooth relationship between response and predictor variable. In general, the smoothing techniques comprise of various methods. Thus, in order to pick the right one, we have to consider the condition of spacing between values of predictor or X variable. The following two techniques are applied in a case of values of X variable are equally separated.
According to our previous Water/Temperature example, we revealed the nature of relationship between temperature and water consumption by plotting a scatter plot. The scatter plot (see figure 1.) of these two variables identified quite clearly that a linear relationship between the two might be the case.
However, life is always full with surprises, in many cases it might be very difficult to perfectly tell the structure of the regression relationship by simply investigating a scatter plot. Let take a look at figure 2. Figure 2 is a scatter plot between number of hours required to finish mowing a given lawn and water consumption
As you can see, it is fairly awkward to visually explain the relationship between these two variables. In this kind of situation, statisticians suggest that we may need to apply a special method: smoothing technique
Fitting smoothed curves is also known as nonparametric regression analysis. This regression analysis requires minimal assumptions of linear least squares regression, for example, it is not necessary to assume linearity between response and predictor variable. The method not only allows us to uncover structure of the data but can be very helpful in checking validity of our fitted least squares regression function as well.
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