What is the strongest linear correlation?

The relationship between two random independently distributed variables is considered to be theoretically the weakest when the correlation coefficient is zero and theoretically the strongest when the correlation coefficient is one, indicating a positive relationship between two variables and negative one, indicating a negative relationationship between two variables.

I state that this is a theoretical result as if variables are not random, independently distributed, then a high correlation coefficient can result. For example, let us say that we obtained the following data on age and frequency of accidents:

Age 18 1 in 18 people have accidents in a year

Age 25 1 in 25 people have accident in a year

Age 30 1 in 30 people have accidents in a year

Age 35 1 in 6 people have accidents.

Age 40 1 in 400 people have accidents

If I selectively calculated a correlation coefficient this data including only the three groups ages 18, 25 and 30, you can see I will have a correlation coefficient of 1, however the data was not a random sample of all ages.

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