This problem comes from Chapter 6 of Johnson (1998). Below is the description from Johnson:

The data in Table 6.2 is taken from Gunst and Mason (1980) and consist of anthropometric and physical fitness measurements that were taken on 50 white male applicants to the police department of a major metropolitan city. The variables include:

1. Reaction time in seconds to a visual stimulus (REACT)
2. The applicant’s height in centimeters (HEIGHT)
3. The applicant’s weight in kilograms (WEIGHT)
4. The applicant’s shoulder width in centimeters (SHLDR)
5. The applicant’s pelvic width in centimeters (PELVIC)
6. The applicant’s minimum chest circumference in centimeters (CHEST)
7. The applicant’s thigh skinfold thickness in millimeters (THIGH)
8. The applicant’s resting pulse rate (PULSE)
9. The applicant’s diastolic blood pressure (DIAST)
10. The number of chin-ups the applicant was able to complete (CHNUP)
11. The applicant’s maximum breathing capacity in liters (BREATH)
12. The applicant’s pulse rate after 5 minutes of recovery from treadmill running (RECVR)
13. The applicants maximum treadmill speed (SPEED)
14. The applicant’s treadmill endurance time in minutes (ENDUR)
15. The applicant’s total body fat measurement (FAT)

The data is in the file police_applicant.csv, using this data, complete the following.

a) Use PCA with the correlation matrix to help choose an initial number of common factors.

b) Using the initial number of common factors from part a), determine the number of common factors to use. Make sure to justify your choice. (examine the appropriate measures to judge their adequacy)

c) Using the varimax method, state the FA model for the number of common factors chosen. Interpret the common factors.

d) Examine and interpret the appropriate plots of the factor scores.

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policeapplicant <- read.table("policeapplicant.txt", sep = ",", header = TRUE)
# [15] "ENDUR" "FAT."
# 50 16
names(policeapplicant)[16] <- "FAT"
# a)
pca.cor<-princomp(x = policeapplicant[,-1], cor = TRUE, scores = TRUE)
summary(pca.cor, loadings = TRUE, cutoff = 0.0)
plot(pca.cor, type = "lines", main = "Scree plot for police applicant data")
screeplot(pca.cor,type="lines", npcs=15)

#Importance of components:
# Comp.1    Comp.2    Comp.3    Comp.4    Comp.5    Comp.6    Comp.7    Comp.8    Comp.9    Comp.10    Comp.11   Comp.12
# Standard deviation    2.2844092 1.5513858 1.14572172 1.10953830 1.09719900 0.92081715 0.8394927 0.76053179 0.62733307 0.60678801 0.57147648 0.4322846
# Proportion of Variance 0.3479017 0.1604532 0.08751188 0.08207168 0.08025638 0.05652695 0.0469832 0.03856057 0.02623645 0.02454611 0.02177236 0.0124580
# Cumulative Proportion 0.3479017 0.5083549 0.59586678 0.67793847 0.75819484 0.81472179 0.8617050 0.90026557 0.92650202 0.95104813 0.97282049 0.9852785
# Comp.13    Comp.14    Comp.15
# Standard deviation    0.37256730 0.209478794 0.195281644
# Proportion of Variance 0.00925376 0.002925424 0.002542328
# Cumulative Proportion 0.99453225 0.997457672 1.000000000...

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