A: Part (a): We can generate a simulated data set with 20 observations in each of the three classes, and 50 variables using uniform or normal distributed samples.
For example, we can generate random numbers between 0 and 1 for each of the 50 variables, and assign a class label to each of the observations. For example, if the value of the first variable is less than 0.34, we can assign it to class A, if it is between 0.34 and 0.67, we can assign it to class B, and if it is greater than 0.67, we can assign it to class C. We can then repeat this process for the other 49 variables.
Part (b): We can then perform PCA on the 60 observations and plot the first two principal component score vectors, using a different color to indicate the observations in each of the three classes.
To perform PCA on the 60 observations and plot the first two principal component score vectors, we can use a scatter plot. We can then assign a different color to each of the three classes, so we can visually see if there is any separation between the classes.
Part (c): If the three classes show at least some separation in the first two principal component score vectors, then we can continue to analyze the data by looking at the other principal component score vectors, and the correlations between the variables.
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