which of the following pairs of variables should produce a c

which of the following pairs of variables should produce a correlation near zero?

1. model year and price of a used honda

2. number of hours studying and number of errors on a math exam

3. IQ and weight of a group of 3rd grade students

4. driving distance and cost of gas for a group of commuting college students

Solution

The correlation is the measure of linear relationship between two variables. So, correlation value close to zero means that they are independent of each other.

However, without the actual data of the variables, it\'s tough to decide whether the correlation is zero or not, as the variables may take any random value.

But, one can tell by intuition whether the variables are correlated or not. Like we can say that the price of a house and the square feet area of the house are correlated (although it\'s not statistically significant to say that).

--------------------------------------------------------------------------------------------------------------------------------------------------------------------In the case 1, the variables \'model year\' and \'price\' of a used honda seem to be correlated as the price of a honda will certainly depend on the model of the bike, and hence the model year. So, they aren\'t independent of each other.

--------------------------------------------------------------------------------------------------------------------------------------------------------------------

In case 2, the variables \'number of hours studying\' and \'number of errors on a math exam\' also must be correlated as the number of error will be less if the number of study hours is more. So, there must be a negative correlation between the two variables.

---------------------------------------------------------------------------------------------------------------------------------------------------------------------

In case 3, the variables \'IQ\' and \'weight\' doesn\'t seem to be correlated as IQ of a person has got nothing to do with his weight. Two person with same weight can have different IQ and two person with same IQ can have different weights. So, these two variables are independent of each other. Hence, the correlation must be close to zero.

-----------------------------------------------------------------------------------------------------------------------------------------------------------------

In the case 4, the variables \'driving distance\' and \'cost of gas\' for a group of commuting college students also will be correlated as the cost will increase with increase in driving distance. Hence, they are positively correlated with each other.

_____________________________________________________________________________________________

Hence, the correct option is option (4).