When we are done with the regression procedure we will plot our "numbers- (I did not explain everything to her right away, just to avoid confusion) in a model for multiple regression with the equation-: .
Amy: "Who taught you all this?-.
Ozan: "Dr. Wiorkowski! But let's get back to work. First of all, as is evident in the name multiple linear regression, it is assumed that the relationship between variables is linear. But as you can imagine, in practice this assumption can never be confirmed; since the real world can never be linear and has "errors-. Fortunately, multiple regression procedures are not greatly affected by minor deviations/errors from this assumption. However, as a rule it is prudent to always look at two-dimensional scatter plots of the variables. If curvature in the relationships is evident, we will have to consider transforming the variables, which, let us hop,e will not be necessary. Excel will help us evaluate the relationship between the "x-values- and "y-values-."".
We started with predicting the model for the Asking Price.
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Decision for Relevant Data.
I plotted the different values of "x- against the "y- (Asking Price) to establish if a relationship exists between each dependant variable and the independent variable and to verify that it is not curvilinear.
Evaluation: Asking Price and Number of Garages .
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This graph did not show any curvature. And outliers could not be detected either. As you might imagine the question, "what is an outlier?- came like a shot. And I had to take a trip down memory lane. .
I tried to explain to her that outliers (extreme cases) can seriously bias the results by "pulling" or "pushing" the regression line in a particular direction, therefore leading to biased regression coefficients. Often, excluding just a single extreme case can yield a completely different set of results. But once again, outliers will only seriously affect our regression analysis if they are consistently extreme cases.
