Individual assignment X

In this assignment we will work with the dataset \(\mathsf{uscrime}\). I created a new binary covariate based on the principal component analysis from the Assignment VI. I merged the regions into two according to the rate of murder and rape. I merged northeast + Midwest and South + West since the rate of these crimes was lower in Northeast and Midwest, and on the contrary higher in South and West. Here we go performing the LDA, starting with histograms for the first LD in both groups:

       
In the second group we can see a higher variability in the LD1 than in the first group. Generally, in the second group we observe higher values of LD1 than in the first group.

We know that from a geometrical point of view, we can consider the LDA as a division of a space. Here we can see the results and also the error rates.

We can see that taking into account robbery and murder, the precision of the prediciton is higher.

For comparison, we will use the linear regression approach:

We can see that the results are exactly the same.