Question: In R , use the data set state.x 7 7 . By only using its Population, Income, and Illiteracy columns, apply the K -

In R

,

use the data set "state.x

77 " .

By only using its "Population", "Income", and "Illiteracy"

columns, apply the K

-

Means Algorithm with

3, 4,

and

5

clusters., then answer the following

questions.

1)

Provide all the necessary codes in R

.

According to the outputs,

2)

What are the sizes of clusters in the

3 -

cluster case?

3)

What are the sizes of clusters in the

4 -

cluster case?

4)

What are the sizes of clusters in the

5 -

cluster case?

5)

For the

3 -

cluster case, give two examples from the cluster, which includes Alabama.

6)

For the

4 -

cluster case, give two examples from the cluster, which includes Alaska.

7)

For the

5 -

cluster case, give two examples from the cluster, which includes Arizona.

8)

Compare the overall quality of the three solutions. Which K value would you select for

this data set? Why?

9)

Visualize your choice in the previous question on a scatter plot

(

Population on the xaxis, Income on the y

-

axis

) .

Provide your R code and the output.

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