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Two horizontal lines are drawn in the figure. We shall explain them closer. The lower horizontal line represents the significance level corresponding to 1% significance. Variables having values above it indi- cate a significant relationship to the response vari- able. In order to find out which variables should be used, we place a horizontal line on the figure and se- lect all the variables, giving a squared correlation co- efficient, r*, higher than the one corresponding to the line. For these variables, we carry out a PLS regres- sion. We start the horizontal line so that we get a few variables, say 3, then we lower the around 20 PLS regressions. In the line. We carry out ast one, we use all the variables. In all 20 PLS regressions, four compo- nents were used. Four components were found ap- propriate for the model having the argest Q7. For the 20 PLS regressions, we compute the R? for the given data and Q? for the test data (the 15 samples). In Fig. 6 we plot the 20 values of R? and Q°. ~~ = ~ There are some aspects of Fig. 6 that are impor- tant to notice. The amount of variables used in the first six PLS regressions are 3, 13, 15, 18, 20 and 50, respectively. All PLS regression were carried out us-

Figure 6 Two horizontal lines are drawn in the figure. We shall explain them closer. The lower horizontal line represents the significance level corresponding to 1% significance. Variables having values above it indi- cate a significant relationship to the response vari- able. In order to find out which variables should be used, we place a horizontal line on the figure and se- lect all the variables, giving a squared correlation co- efficient, r*, higher than the one corresponding to the line. For these variables, we carry out a PLS regres- sion. We start the horizontal line so that we get a few variables, say 3, then we lower the around 20 PLS regressions. In the line. We carry out ast one, we use all the variables. In all 20 PLS regressions, four compo- nents were used. Four components were found ap- propriate for the model having the argest Q7. For the 20 PLS regressions, we compute the R? for the given data and Q? for the test data (the 15 samples). In Fig. 6 we plot the 20 values of R? and Q°. ~~ = ~ There are some aspects of Fig. 6 that are impor- tant to notice. The amount of variables used in the first six PLS regressions are 3, 13, 15, 18, 20 and 50, respectively. All PLS regression were carried out us-

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It shows that the samples represent smooth curves as functions of the variable number. At both ends the samples show larger variation. At the lower end we see larger variation in the curves, while at the higher end we see some instrumental noise. The response In this work we search for intervals that should be used in the analysis. The reason for finding intervals instead of individual variables is that it is useful to get as large score vectors as possible. Score vectors based on intervals are larger than the ones based on vari- ables and thus give more stable predictions. The lit- erature on variable selection is very large, but very little has been done on finding intervals. In Ref. [2] the variables are divided into a number of intervals and a PLS regression is carried out at each interval. By working with sufficiently many (or small) inter- vals, this approach is useful in finding the interval that we should work with. The importance of the present work is due to that the procedures can be used in au-
It shows that the samples represent smooth curves as functions of the variable number. At both ends the samples show larger variation. At the lower end we see larger variation in the curves, while at the higher end we see some instrumental noise. The response In this work we search for intervals that should be used in the analysis. The reason for finding intervals instead of individual variables is that it is useful to get as large score vectors as possible. Score vectors based on intervals are larger than the ones based on vari- ables and thus give more stable predictions. The lit- erature on variable selection is very large, but very little has been done on finding intervals. In Ref. [2] the variables are divided into a number of intervals and a PLS regression is carried out at each interval. By working with sufficiently many (or small) inter- vals, this approach is useful in finding the interval that we should work with. The importance of the present work is due to that the procedures can be used in au-
Variation found in first 10 components in PLS regression Table 1
Variation found in first 10 components in PLS regression Table 1
Variation found in first 10 components in PLS regression. 80 vari- ables
Variation found in first 10 components in PLS regression. 80 vari- ables
Fig. 4. Plot of squared correlation coefficients, r?, vs. variable no. NIR data are important in the analysis of food and agricultural data. This example shows that it is im- portant to remove or eliminate the ‘ends’ of the data. We have used here the squared of the simple cor- relation coefficient, r, between a variable (a column in X) and y. Other measures of correlation could also be used. The figure shows that there are a few ‘inter- vals’, where the values of the squared correlation co- efficient are large. Values above the horizontal line
Fig. 4. Plot of squared correlation coefficients, r?, vs. variable no. NIR data are important in the analysis of food and agricultural data. This example shows that it is im- portant to remove or eliminate the ‘ends’ of the data. We have used here the squared of the simple cor- relation coefficient, r, between a variable (a column in X) and y. Other measures of correlation could also be used. The figure shows that there are a few ‘inter- vals’, where the values of the squared correlation co- efficient are large. Values above the horizontal line
Fig. 5. Plot of squared correlation coefficients, r*, versus variable no. Two horizontal lines.
Fig. 5. Plot of squared correlation coefficients, r*, versus variable no. Two horizontal lines.
Cumulative R? value for 0 to 5 OSC components (horizontal). Up to eight PLS components Table 3
Cumulative R? value for 0 to 5 OSC components (horizontal). Up to eight PLS components Table 3
Fig. 7. Squared simple correlation coefficient, r?, for reduced X and y, when X has been reduced by one, two, three and four OSC compo- nents.
Fig. 7. Squared simple correlation coefficient, r?, for reduced X and y, when X has been reduced by one, two, three and four OSC compo- nents.
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