Choose the correct answer for each question. You must click on the link for the details of the analysis.

1. Why undertake a principal components analysis on these predictors?

   1.   ?    Because there are too many predictors.
   2.   ?    Because the predictors have different measurement scales.
   3.   ?    Because they are highly correlated.
   4.   ?    Because it will simplify the interpretation.
   5.   ?    Because it will decrease the incorrect predictions.

2. Why were 2 components extracted?

   1.   ?    Because this is the default option for a PCA.
   2.   ?    Because this would halve the number of predictors, thus reflecting the use of petal and sepal characters.
   3.   ?    A default analysis would extract only 1 component. However, the second eigenvalue is close to 1 and extracting it will retain almost 96% of the original variation.
      

3. How much of the original variation is retained by two factors?

   1.   ?    77.962%
   2.   ?    22.851%
   3.   ?    100%
   4.   ?    95.183%

4. What is the structure of the 2 components?

   1.   ?    Function 1 is everything. Function 2 is everything except PETAL_L.
   2.   ?    Function 1 is everything except SEPAL_W.
      Function 2 is mainly SEPAL_W.
   3.   ?    Function 1 is the petal characters, Function 2 is the sepal characters.
   4.   ?    Function 1 is SEPAL_W and Function 2 is SEPAL_W and SEPAL_L

5. Examine the plot of the factor scores. What does it suggest about the possibility of discriminating between the species using PC scores?

   1.   ?    PC1 separates setosa very well, it also marginally separates the other two. So this should be the better discriminator. PC2 again marginally separates versicolor and virginica.
   2.   ?    PC1 again marginally separates versicolor and virginica. PC2 separates setosa very well, it also marginally separates the other two. So this should be the better discriminator.
   3.   ?    It will not be possible to separate out the three species using either function.

6. What is the maximum of discriminant functions that could be extracted during this analysis?

   1.   ?    1
   2.   ?    2
   3.   ?    3

7. How many significant discriminant functions were extracted?

   1.   ?    0
   2.   ?    1
   3.   ?    2

8. What are the structures of the functions?

   1.   ?    Function 1 is almost entirely PC2, whilst Function 2 is perfectly correlated with PC1.
   2.   ?    Function 1 is both PC1 and PC2, whilst Function 2 is perfectly mainly PC2.
   3.   ?    Function 1 is almost entirely PC1, whilst Function 2 is perfectly correlated with PC2.
   4.   ?    They make an equal contribution to both functions.

9. 6. Which species does each function separate?

   1.   ?    Function 1 separates setosa from the other two. Function 2 separates versicolor from virginica.
   2.   ?    Function 1 separates versicolor from the other two.
      Function 2 separates virginica from the other two.
   3.   ?    All three are equally separated by both functions,

10. How many cases were correctly classified using cross validation?

    
    
    CheckHintShow answer

11. Which two species were most frequently misclassified?

    1.   ?    Setosa and virginica
    2.   ?    Setosa and versicolor
    3.   ?    Versicolor and virginica
    4.   ?    Equal misclassifications

12. Which of the 3 analyses would you consider the 'best'?

    1.   ?    The first one using the 4 original predictors.
    2.   ?    The stepwise method.
    3.   ?    This one, using the PC scores.