women who reported an earlier age at menarche were more likely to be heavier at age...

women who reported an earlier age at menarche were more likely to be heavier at age 7 years (average weight = 24.7 kg) compared with those who reported a later age at menarche (average weight = 23.2 kg) (P = 0.01). The correlation between weight at age 7 years and age at menarche was -0.17 (P = 0.009).

Q: The -0.17 value is for what? how to find it and why it is important to mention?

Expert Solution

The above value of correlation coefficient -0. 17 indicates that the there is slightly negative correlation between the weight at age 7 and age at menarche. The one who is reported menarche at latter age less weight as compare to one who reported an earlier age menarche.

Simply, the latter age menarche implies the less wight.

That is there is inverse relationship between them.

The correlation coefficient is very important because it measures the linear relationship between two variables.

A correlation coefficient of 1 means that for every positive increase in one variable, there is a positive increase of a fixed proportion in the other. For example, shoe sizes go up in (almost) perfect correlation with foot length.
A correlation coefficient of -1 means that for every positive increase in one variable, there is a negative decrease of a fixed proportion in the other. For example, the amount of gas in a tank decreases in (almost) perfect correlation with speed.
Zero means that for every increase, there isn’t a positive or negative increase. The two just aren’t related.

We can find it using any statistical softwaresoftware or Manually using formula.

The formula to find correlation coefficient is as follows,

In the above formula n= no of observation

X and Y are the two variables who's correlation coefficient we have to find.

r denote the correlation coefficient.

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