Acknowledgments
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| From the formula, you can tell that these calculations will be tedious. However, one can construct various useful plots involving them. This method is most often used when doing a multiple regression analysis, which will be included in this particular project [2].
While residual plots often help to determine the appropriateness of the model chosen, difficulties may arise. In reality, the residual plot may not have a random dispersion of residual values. In this case, a nonlinear model may be more appropriate. Perhaps the chosen model appears to fit the data fairly well, with the exception of a few outlying values. These values may be drastically manipulating the model of the best-fit function. Excluding those outliers in the data set could lead to a change in the original model. However, this is harder to determine when working with multiple regression models [2]. Lastly, the model could possibly be a poor fit if one or multiple independent variables were not considered or included in the data set. An example of this case can be seen when there is a pattern in the residuals when the residuals are plotted against an omitted variable. From this, one can incorporate the omitted variable in a multiple regression model [2]. As you can see there are some modifications that can be made in order to correct some of the obscurities found in residual plots. MULTIPLE REGRESSION In the simple case of regression, the only concern was with the correlation between two variables. However, this simple case can now be generalized into the multiple regression case. One would use multiple regressions to build a model that relates numerous independent variables to a single dependent variable [2]. For instance, suppose that the high school grade point average and SAT score were thought to be a good predictor of a student’s college grade point average. If a model was to be constructed to help support this claim, it would be a multiple regression model. Let n represent the number of independent or “predictor variables” that wish to be studied, where n has to be at least two. Denote these predictor variables as  . Then the general additive multiple regression model equation is
where  and . It is also assumed that  is normally distributed.
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