Multivariate Regression Compared with Moving Average Smoothing

Regression analysis is a statistical method having application in all fields of scientific and technological studies. Theoretical concepts lead to the development of regression theory are examined in some detail to lay down the foundation for the application of the theory. In statistics regression is mainly used to establish the kind of relationship between dependent and independent variables, i.e. linear or any other type. Moving average is a statistical method widely used for smoothing out raw data trajectories to obtain trends by filtering out the noise from the random fluctuations. The trend is an estimation of the functional behavior of the variable under study. This thesis is first centered on the theoretical characteristics of linear regression in chapter 3, examining the abstract concepts behind the regression theory, and the least squares method for establishing the model to be fitted from available data. Chapter 4 is allocated for the moving average technique used as a smoother of the trajectory for a variable. That smooth trend can be generated for every variable. The fitted regression model itself can be considered a smooth functional representation of the response variable in relation to the predictor/s. In Chapter 5 a case study of a data set is undertaken, where moving average technique was implemented for smoothing with 2 different orders, using m = 3 and m = 6 values for averaging of a real life data. It became evident that the smoother the data, the lower the error measures will be in a regression analysis. However, too much smoothing of a variable will runs the risk of obtaining close to a perfect regression fit, which will not be realistic. Based on the results obtained in the case study, it was then recommended that where large data sets are used for regression study, some smoothing can be beneficial as it will result in reduced estimation errors. Some software programs like Excel, Minitab, and S.P.S.S were all used to help in data processing to find the needed outputs.