Sketch a scatterplot where the association is nonlinear, but the correlation is close to [r = -1].

Tobias Ali 2020-10-26 Answered

Sketch a scatterplot where the association is nonlinear, but the correlation is close to [r=1].

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Alannej
Answered 2020-10-27 Author has 104 answers

An association is nonlinear when there is some curvature present in the scatterplot.
The correlation is close to [r=1], when the pattern slopes downwards strongly and the points do not deviate much from this sloping downwards pattern.
For example, the following graph then has a correlation close to [r=1] while also being nonlinear (note: The correlation of this particular graph is 0.8941).

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New questions

Euclid's view and Klein's view of Geometry and Associativity in Group
One common item in the have a look at of Euclidean geometry (Euclid's view) is "congruence" relation- specifically ""congruence of triangles"". We recognize that this congruence relation is an equivalence relation
Every triangle is congruent to itself
If triangle T 1 is congruent to triangle T 2 then T 2 is congruent to T 1 .
If T 1 is congruent to T 2 and T 2 is congruent to T 3 , then T 1 is congruent to T 3 .
This congruence relation (from Euclid's view) can be translated right into a relation coming from "organizations". allow I s o ( R 2 ) denote the set of all isometries of Euclidean plan (=distance maintaining maps from plane to itself). Then the above family members may be understood from Klein's view as:
∃ an identity element in I s o ( R 2 ) which takes every triangle to itself.
If g I s o ( R 2 ) is an element taking triangle T 1 to T 2 , then g 1 I s o ( R 2 ) which takes T 2 to T 1 .
If g I s o ( R 2 ) takes T 1 to T 2 and g I s o ( R 2 ) takes T 2 to T 3 then h g I s o ( R 2 ) which takes T 1 to T 3 .
One can see that in Klein's view, three axioms in the definition of group appear. But in the definition of "Group" there is "associativity", which is not needed in above formulation of Euclids view to Kleins view of grometry.
Question: What is the reason of introducing associativity in the definition of group? If we look geometry from Klein's view, does "associativity" of group puts restriction on geometry?