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

1. The communality for Age is very small. What does this mean and why should it be so small?

   1.   ?    Age is uncorrelated with the other variables.
   2.   ?    Age is highly correlated with other variables.
   3.   ?    Age has a small variance
   4.   ?    Age has a small coefficient of variation (standard deviation / mean).

2. How many factors are extracted and what is the total amount of variation that is retained by them?

   1.   ?    6 factors extracted 100% of the variation.
   2.   ?    3 factors extracted 100% of the variation.
   3.   ?    3 factors extracted 72.9% of the variation.
   4.   ?    3 factors extracted 22.1% of the variation.
   5.   ?    6 factors extracted 72.9% of the variation.

3. How many factors do think should be extracted?

   1.   ?    6
   2.   ?    2
   3.   ?    3
   4.   ?    4

4. Which of the following best describes the variable loadings on the inital components?

   1.   ?    1. AGE & WBC
      2. WT & AGE
      3. WT & AGE
   2.   ?    1. All except AGE & WBC
      2. All except WT & AGE
      3. All except WT & AGE
   3.   ?    1. BMI & WT
      2. WT & HT
      3. MCV & WBC
   4.   ?    1. All except WBC & MCV
      2. All except HT
      3. All except BMI

5. Which of the following best describes the variable loadings on the rotated components?

   1.   ?    1. All except AGE & WBC
      2. All except WT & AGE
      3. All except WT & AGE
   2.   ?    1. All except MCV
      2. All except BMI & WBC
      3. GE, MCV and WBC
   3.   ?    1. BMI
      2. HT
      3. MCV
   4.   ?    1. BMI & WT
      2. WT & HT
      3. MCV & WBC

6. Using the loading patterns which of the following might be suitable 'names' for the three rotated components.

   1.   ?    PC1, PC2 and PC3
   2.   ?    Factor 1 = obesity
      Factor 2 = size
      Factor 3 = blood characteristics.
   3.   ?    Factor 1 = size
      Factor 2 = height
      Factor 3 = blood characteristics.
   4.   ?    The loadings don't give any clear picture. There are no sensible names.

7. Which variable has the lowest loading on all three components?

   1.   ?    BMI
   2.   ?    WT
   3.   ?    AGE
   4.   ?    HT
   5.   ?    MCV
   6.   ?    WBC

8. What do you think will happen if a fourth factor is extracted?

   1.   ?    AGE will have a large loading on the fourth factor.
   2.   ?    Impossible to say.
   3.   ?    All of the variables will be loaded on a fourth factor.

9. Examine the scatter plot of factor scores (Factors 1 and 2). Which of the following best describes the patterns illustrated in this plot? The descriptions relate to the four quadrants: Upper Left, Upper Right, Lower Left, Lower Right (The boundaries are the means for the two factor scores).

   1.   ?    Thin and 'large', mainly males
      Thin and 'small', mainly females
      Obese and 'small', mainly females
      Obese and large, mainly males
   2.   ?    Thin and 'small', mainly females
      Obese and 'small', mainly females
      Thin and 'large', mainly males
      Obese and large, mainly males
   3.   ?    Thin and 'large', mainly males
      Obese and large, mainly males
      Thin and 'small', mainly females
      Obese and 'small', mainly females
   4.   ?    Thin and 'large', mainly females
      Obese and large, mainly females
      Thin and 'small', mainly males
      Obese and 'small', mainly males

10. Examine the communalities from the second analysis (4 factors extracted). How and why have they changed from the previous analysis?

    1.   ?    There were no major changes.
    2.   ?    Age has a much bigger communality.
    3.   ?    All of the communalities have increased.

11. How much extra variation is retained when the fourth factor is extracted?

    1.   ?    16.2%
    2.   ?    88.9%
    3.   ?    99.76%
    4.   ?    18.51%

12. Has the amount of variation associated with the first three factors been affected by the extraction of the fourth factor?

    1.   ?    No
    2.   ?    Yes

13. Examine the pattern of rotated factor loadings. Identify, and name (if possible) the four factors.

    1.   ?    Factor 1 = obesity
       Factor 2 = size
       Factor 3 = blood characteristics
       Factor 4 = mixed
    2.   ?    Factor 1 = obesity
       Factor 2 = size
       Factor 3 = blood characteristics
       Factor 4 = age
    3.   ?    Factor 1 = size
       Factor 2 = height
       Factor 3 = blood characteristics
       Factor 4 = age
    4.   ?    Factor 1 = age
       Factor 2 = obesity
       Factor 3 = size
       Factor 4 = blood characteristics