Question

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For each of Questions 1 to 5, is the given value of the correlation coefficient reasonable?

Hint: think about the strength and the direction of the relationship between the two variables in each case.

Note: It is subjective to decide whether the magnitude of the correlation between two variables should be, for example, 0.7 or 0.8. The below questions don't ask you to make a decision like this.

Question 1 

A correlation of r = +0.7 between gender and height.

	Reasonable
	Not reasonable

Question 2 

Let X = speed of vehicles driving on the highway and Y = distance for the vehicles to stop when the brakes are applied.

A correlation of r = +1.0 between X and Y.

	Reasonable
	Not reasonable

Question 3 

A correlation of r = 0 between number of slurpees (a frozen beverage) sold at 7-Eleven in one day and number of cups of hot chocolate sold at the same store in the same day.

	Reasonable
	Not reasonable

Question 4

A correlation of r = +0.7 between number of pages in a fiction novel and time it takes to read the novel.

	Reasonable
	Not reasonable

Question 5 

Let X = time it takes a marathon runner to finish the race and Y = number of runners who finish ahead of him.

A correlation of r = -0.8 between X and Y.

	Reasonable
	Not reasonable

Answer 1

Question 1

On average, males are taller than females. So, the correlation of r = +0.7 between gender and height seems reasonable.

Question 2

The distance for the vehicles to stop when the brakes are applied will increase with increase in speed of vehicles driving on the highway. There may be strong positive correlation between X and Y close to +1.0. Thus, correlation of r = +1.0 between X and Y seems reasonable.

Question 3

Number of slurpees (a frozen beverage) sold at 7-Eleven in one day may be high in summer season and low in cold season. Number of cups of hot chocolate sold at the same store may be low in summer season and high in cold season. Hence the correlation r should be negative. A correlation of r = 0 between number of slurpees (a frozen beverage) sold at 7-Eleven in one day and number of cups of hot chocolate sold at the same store in the same day seems Not reasonable.

Question 4

More number of pages in a fiction novel and will take more time to read the novel. A correlation of r = +0.7 between number of pages in a fiction novel and time it takes to read the novel seems reasonable.

Question 5

The time it takes a marathon runner to finish the race will increase with increase in number of runners who finish ahead of him. The last runner will take the maximum time and all runners will finish ahead of him. The first runner will take the minimum time and no runners will finish ahead of him. So, there will be positive correlation between X and Y. A correlation of r = -0.8 between X and Y seems Not reasonable.