Identify what is wrong with each of the following statements: a) The correlation

Question

Identify what is wrong with each of the following statements: a) The correlation between Olympic gold medal times for the 1500m run and year is -0.941 seconds per year. b) The correlation between Olympic gold medal times for the 1500m run and year is -1.941 c) Because the correlation between Olympic gold medal times for the 1500m run and year is -0.941, the correlation between year and Olympic gold medal times for the 1500m run is +0.941. d) If we were to measure Olympic gold medal times for the 1500m run in minutes instead of seconds, the correlation would be -0.941/60-0.016.

Explanation / Answer

a) It is given that correlation between olympic gold medal times for the 1500m run and year is -0.941 seconds for year.

r(X,Y)= -0.941 which is a negative correlation.

We know that correlation coefficient lies between -1 and +1.

From this result we can intrepret that as year increases olympic gold medal times for the 1500m run decreases and vice versa.

This is correct.

b)Here,it is given that the correlation between olympic gold medal times for the 1500m run and year is -1.941.

We know that correlation coefficient lies between -1 and +1.

Here,correlation coefficient crosses it's limit so,this is false.

c)Correlation is symmetrical with respect to x and y.

i.e., r(X,Y)=r(Y,X)

But here it is saying that r(X,Y)= -0.941

r(Y,X)= +0.941

r(X,Y) is not equal to  r(Y,X)

Hence this is false.

d)cov(ax,y)=acov(x,y)

or

Usually when we converting minutes into seconds we will divide it by 60.

Here,also we have did the same thing.

Hence this is correct.

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