MVA

# Creating the data frame
df <- data.frame(
  ID = c("046", "149", "096", "064", "050", "210", "082", "121"),
  Groupa = c("P", "A", "A", "P", "A", "A", "P", "P"),
  Baseline = c(30.8, 26.5, 25.8, 24.7, 20.4, 20.4, 28.6, 33.7),
  Week_1 = c(26.9, 14.8, 23.0, 24.5, 2.8, 5.4, 20.8, 31.6),
  Week_4 = c(25.8, 19.5, 19.1, 22.0, 3.2, 4.5, 19.2, 28.5),
  Week_6 = c(23.8, 21.0, 23.2, 22.5, 9.4, 11.9, 18.4, 25.1)
)

# Displaying the data frame
df

##    ID Groupa Baseline Week_1 Week_4 Week_6
## 1 046      P     30.8   26.9   25.8   23.8
## 2 149      A     26.5   14.8   19.5   21.0
## 3 096      A     25.8   23.0   19.1   23.2
## 4 064      P     24.7   24.5   22.0   22.5
## 5 050      A     20.4    2.8    3.2    9.4
## 6 210      A     20.4    5.4    4.5   11.9
## 7 082      P     28.6   20.8   19.2   18.4
## 8 121      P     33.7   31.6   28.5   25.1

#Generate means,covariance and correlation

# Calculate column means based on Groupa
col_means <- aggregate(. ~ df[, 2], data = df[, 3:6], FUN = mean)
print("Column Means:")

## [1] "Column Means:"

print(col_means)

##   df[, 2] Baseline Week_1 Week_4 Week_6
## 1       A   23.275  11.50 11.575 16.375
## 2       P   29.450  25.95 23.875 22.450

# Calculate the covariance matrix
cov_mat <- cov(df[, 3:6])
print("Covariance Matrix:")

## [1] "Covariance Matrix:"

print(cov_mat)

##          Baseline    Week_1   Week_4   Week_6
## Baseline 21.81982  42.46393 39.43107 22.34054
## Week_1   42.46393 105.01357 91.27643 56.33393
## Week_4   39.43107  91.27643 84.66786 51.60393
## Week_6   22.34054  56.33393 51.60393 33.67268

# Calculate the correlation matrix
cov_mat <- cov(df[, 3:6])
print("Correlaton Matrix:")

## [1] "Correlaton Matrix:"

cor_mat<-cov2cor(cov_mat)
print(cor_mat)

##           Baseline    Week_1    Week_4    Week_6
## Baseline 1.0000000 0.8870985 0.9173894 0.8241934
## Week_1   0.8870985 1.0000000 0.9680029 0.9473457
## Week_4   0.9173894 0.9680029 1.0000000 0.9664617
## Week_6   0.8241934 0.9473457 0.9664617 1.0000000