In 1973, Francis Anscombe, a famous statistics lecturer who reasearched the need for randomization in experimental design and analysis, used the following four sets of data to illustrate the need for visual inspection of data. Each data set has a paired set of values; (x1, y1) for the first set, (x2, y2) for the second, …, and (x4, y4) for the fourth. Use this Investigative Task 1 to discover why calculations we are practicing in this course do not give enough information to summarize an association.

You will perform/answer the following tasks by following each of the steps in the rubric below.

What are each of the four correlation coefficients?
• Attach a table of only the necessary summary statistics for each data set,
• illustrate (type) the initial calculation of one of the correlation coefficients, and
• then attach a summary table with each of the four correlation values.

What do the four calculations lead you to conclude?

Next create and insert four scatterplots, one for each of the corresponding data sets.

Use the scatterplots you've posted to describe the distinctiveness of each relation. Why is each one different than the others? Be sure to use the lesson's vocabulary to explain why each association is different than the other associations.

Summarize this investigation by writing and completing the following two sentences:
"Calculating a correlation can help describe a relation between two quantitative variables' ___ and ___ .
However, it is not sufficient to use a correlation coefficient to describe two variables. The addition of ___ can provide other helpful details such as __ _."

Data set 1. 06 Anscombe's quartet [Info]

x1	y1	x2	y2	x3	y3	x4	y4
10	8.04	10	9.14	10	7.46	8	6.58
8	6.95	8	8.14	8	6.77	8	5.76
13	7.58	13	8.74	13	12.74	8	7.71
9	8.81	9	8.77	9	7.11	8	8.84
11	8.33	11	9.26	11	7.81	8	8.47
14	9.96	14	8.1	14	8.84	8	7.04
6	7.24	6	6.13	6	6.08	8	5.25
4	4.26	4	3.1	4	5.39	19	12.5
12	10.84	12	9.13	12	8.15	8	5.56
7	4.82	7	7.26	7	6.42	8	7.91
5	5.68	5	4.74	5	5.73	8	6.89