Three problems of data analysis

Problem 1 (Anscombe's quartet).

Here are four bivariate data sets (numered I-IV), each with n=11 data points.

I.
x	y
10	8.04
8	6.95
13	7.58
9	8.81
11	8.33
14	9.96
6	7.24
4	4.26
12	10.84
7	4.82
5	5.68

II.
x	y
10	9.14
8	8.14
13	8.74
9	8.77
11	9.26
14	8.10
6	6.13
4	3.10
12	9.13
7	7.26
5	4.74

III.
x	y
10	7.46
8	6.77
13	12.74
9	7.11
11	7.81
14	8.84
6	6.08
4	5.39
12	8.15
7	6.42
5	5.73

IV.
x	y
8	6.58
8	5.76
8	7.71
8	8.84
8	8.47
8	7.04
8	5.25
19	12.50
8	5.56
8	7.91
8	6.89

For each data set, compute the means of x and y, the equation of the best fitting linear regression of y onto x, and the correlation coefficient of x and y. Then try to describe what interesting features of each data set, if any, these statistics fail to capture.

Problem 2.

The data for this problem (available here) consist of n=350 data points, each measured on 6 different variables. Without knowing anything about where these values come from or what the variables mean, try to describe what, if any, structure exists in the data.

How do the data points relate to each other? Do they fall naturally into any groups? Are there in any sense fewer data points than meet the eye?

How do the variables relate to each other? Do they fall naturally into any groups? Are there in any sense fewer variables than meet the eye?

Problem 3.

There is a secret message hidden in this set of n=120 data points measured on 4 variables (available here ). Can you find it?