Correlation question. Explain what this sentence mean?

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qwert

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Correlation question. What does this sentence mean? Help!

|r| is close to 1 does not necessarily imply a linear relationship between the two variables.

And if possible, can somebody me how i should answer this question?
The value of r for a sample is +1. Explain why this need not imply that a linear relationship holds for the whole population.

Thank you very much! :)
Please help me this is giving me a huge headache.
 
Last edited:
qwert said:
|r| is close to 1 does not necessarily imply a linear relationship between the two variables.

And if possible, how should i answer this question?

The value of r for the sample is +1. Explain why this need not imply that a linear relationship holds for the whole population.
Click to expand...

The value of r being +1 means, for that particular sample, all of the sample data points lie on the same line. So there might
be other samples who data points that all lie on one line, but it could be a different line from the first sample data points.

If the linear regression correlation coefficient were to be +1 for the population data, then all possible sets of sample data
points would lie on the same line.

However, if all the data points in a particular sample lie on the same line (r for that = +1), that doesn't preclude
any remaining unpicked data points not used in the sample for lying on a different line.


For example, in the x-y plane, let the data points for the population be A(0,0), B(10, 10), C(20, 20), D(30, 10), and E(40, 0).

If you were to choose samples of size 3, there are two sample sets {A, B, C} and {C, D, E} which each respectively have r = +1.
But there exists no linear relationship for the whole population.
 
Last edited:
lookagain said:
The value of r being +1 means, for that particular sample, all of the sample data points lie on the same line. So there might
be other samples who data points that all lie on one line, but it could be a different line from the first sample data points.

If the linear regression correlation coefficient were to be +1 for the population data, then all possible sets of sample data
points would lie on the same line.

However, if all the data points in a particular sample lie on the same line (r for that = +1), that doesn't preclude
any remaining unpicked data points not used in the sample for lying on a different line.


For example, in the x-y plane, let the data points for the population be A(0,0), B(10, 10), C(20, 20), D(30, 10), and E(40, 0).

If you were to choose samples of size 3, there are two sample sets {A, B, C} and {C, D, E} which each respectively have r = +1.
But there exists no linear relationship for the whole population.
Click to expand...



Amazing! I finally got it! Thanks alot lookagain:)
 
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