Question 16 of 19intermediate💡 UnderstandShort Answer3 marks

Interpret the values of r as 1, -1 and 0.

Correct Answer

When r = 1, the correlation is perfect positive. There is an exact linear relation between the two variables, meaning they move in the same direction proportionally.

When r = -1, the correlation is perfect negative. There is an exact linear relation but the variables move in opposite directions. A change in one variable is associated with change in the other in the opposite direction.

When r = 0, the two variables are uncorrelated. There is no linear relation between them. However, this does not rule out the possibility of other types of relations, such as non-linear relations, existing between the variables.

Exercise: EXERCISES | Q: 16 | (Page 16)
For More Understanding

Explanation

The textbook clearly states the interpretation of these three specific values of correlation coefficient. r = 1 and r = -1 both indicate perfect correlation with exact linear relationship - the difference being the direction of relationship. r = 0 indicates absence of linear correlation, but importantly, the textbook clarifies that non-linear relations may still exist. This is a common exam question testing students' understanding of extreme values of correlation coefficient.