Interval for the Entire Regression Model

There are many cases in which a researcher would like to map out the entire regression model (including both bo and hi) with a 1-a Cl. If the data have excess variability, the Cl will be wide. In fact, it may be too wide to be useful. If this occurs, the experimenter may want to rethink the entire experiment or conduct it in a more controlled manner. Perhaps more observations—particularly replicate observations—will be needed. In addition, if the error (y — y) = e values are not patternless, then the experimenter might transform the data to better fit the regression model to the data. 

The F distribution (Table C) is used in this procedure, instead of the t table, where 

Note that the latter is the same formula (2.22) used previously to perform a 1-a Cl for the expected (mean) value of a specific y, on a specific x,. However, the Cl in this procedure is wider than the previous Cl calculations, because it accounts for all x, values simultaneously. 

Example 2.5 Suppose the experimenter wants to determine the 95% Cl for the data in Example 2.1, using the x, values, x, = 0, 15, 30, 45, and 60 sec, termed Xpredicted or p- The y, values predicted, in this case, are to predict the average value of the y,s. The linear regression formula is 

Putting these together, one can construct a simultaneous 1 - a Cl for each Xp  

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