F-to-enter

EQUATION NUMBER (DEPENDENT VARIABLE) Step Variable Entered F to Enter Variable P Step Variable Entered F to Enter Variable P... 

Figure 7.4 Authentication of monovarietal virgin olive oils results of applying stepwise linear discriminant analysis to volatile compounds. Classification was carried out by four volatiles (F)-2-hexenal, butyl acetate, (F)-3-hexenal, 2-methyl-3-buten-2-ol. F-to-Enter was 8.0 tolerance was upper 0.52 for all selected volatiles. Note A, cv. Arbequina C, cv. Coratina K, cv. Koroneiki P, cv. Picual (source SEXIA Group-Instituto de la Grasa, Seville, Spain).

Table 15 Forward regression analysis of the data from Table 11. After three steps no remaining variable has a F-to-enter value exceeding the declared minimum of 4.60, and the procedure stops...

The first selection procedure we discuss is stepwise regression. We have dime this earlier, but not with a software package. Instead, we did a number of partial regression contrasts. Briefly, the F-to-Enter value is set, which can be interpreted as an Ft value minimum for an jc,- variable to be accepted into the final equation. That is, each x,- variable must contribute at least that level to be admitted into the equation. The variable is usually selected in terms of entering one variable at a time with n — k ldf. This would provide an Ft at a = 0.05 of Ft(o.o5,i,ii) = 4.84. The F-to-Enter (sometimes referred to as F in ) is arbitrary. For more than one x,- variable, the test is the partial F test, exactly as we have done earlier. We already know that only X2 would enter this model, because SSr sequential for X2 = 28.580 (Section C, Table 10.2). 

The F-to-Remove command is a set Ft value such that, if the F value is lesser than the F-to-Remove value, it is dropped from the model. The defaults for F-to-Enter and F-to-Remove are F = 4.0 in MiniTab, but can be easily changed. F-to-Remove, also known as Fqut> is a value lesser than or equal to F-to-Enter that is, F-to-Enter > F-to-Remove. 

Forward selection operates using only the F-to-In value, bringing only those x, variables into the equation that have Fc values exceeding the F-to-Enter value. It begins with bo in the model, then sequentially adds variables. In the example, we use F-to-Enter = 4.0, and set F-to-Remove = 0. That is, we are only bringing x, variables into the model that contribute at least 4.0, using the F table. Table 10.4 presents that forward selection data. 

Method forward selection F-to-enter 4.0 F-to-remove 4.0 Step 0 ... 

Adding variable Production with F-to-enter = 7.89159 2 variables in the model. 17 d.f. for error. 

For a furnace temperature of 1600 F, this equation says to use 740 + 0.758 x 1600 = 740 -I- 1213 = 1950°F to enter figures 5.1 or 5.2. This agrees with Figure 5.3, but other conditions will be too low by equation 5.1 (especially with high velocity and low furnace temperature) and too high with low velocities. Use equation 5.1 only with careful judgment. 

Now, starting in column A, say AlO, use EF /BF /F to enter a series of times, in 0.1-min. intervals from about 2 to 15, and enter formulas for Ca, C3, etc. in successive columns using the formula in Equation 17-5. A seventh column can be written which is the sum of all the C values at each time. As seen in the figures, curves for five of the six components are shown, as well as the envelope of all six present. Mixtures having more than six components can also be solved this way, even though the limitation of the graphics restricts us to a total of six separate curves, so a selection must be made for viewing. 

Selection Regression with an F-to Enter Stopping Rule. 

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