Using -Ratios -Statistics for Individual Parameter Significance

5 Using f-Ratios (f-Statistics) for Individual Parameter Significance 

When choosing an arbitrary function to fit a set of data (such as the quadratic in Example 7.2), it might be asked if all three terms in the equation are needed or if it can be simplified by dropping perhaps the linear term (the one involving C2X). To answer this question, statistics gives the answer. It can be shown that the ratio of the optimal parameter values divided by their standard deviations (as determined by Equation 7.7) has a f-distribution with tij-n-1 degrees of freedom. That is. 

Consider again the quadratic function fit to the drying time data of Example 7.2. 

In what follows, each of the statistical tools for determining the quality of the fit is demonstrated. 

With only 9 data points, the data distribute nicely about zero, and the magnitude does not (visually) appear to be a function of x. It can be concluded that the fit is adequate. Note that a single point with a very large residual is a candidate outlier and might be omitted if this can be justified (poor experimental procedure, other extenuating circumstances, etc.). Elowever, the arbitrary exclusion of outliers must be avoided. 

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