Correct option is D
Explanation-
The Pearson correlation coefficient is a statistical measure that describes the strength and direction of a linear relationship between two variables.
Its value ranges from -1 to +1:
Value of r
+1 - Perfect positive linear correlation — as one variable increases, the other also increases in a straight-line relationship
0 - No linear correlation
-1 - Perfect negative linear correlation — as one variable increases, the other decreases in a straight-line relationship
If r is close to -1, this tells us:
1. The two variables are strongly negatively correlated
2. The relationship is linear — meaning the data points lie (or nearly lie) on a straight line
3. As one variable increases, the other decreases
For example: if studying hours increase, stress level might decrease
So, it's not exponential, not random, and not positive correlation — it's a strong inverse linear relationship.
Option D: "There is a linear relationship in which, when there is an increase in one variable, there is a decrease in the second variable."
This is exactly what a strong negative correlation (r ≈ -1) means. It correctly identifies the relationship as linear and the direction as negative (one increases, the other decreases)
Incorrect options-
Option A: "There is no relationship between the two variables"
r ≈ 0 would indicate no relationship, not r ≈ -1.
Option B: "There is an exponential relationship between the two variables"
Pearson's r only measures linear relationships, not exponential ones.
Option C: "There is a linear relationship in which when there is a decrease in one variable, there is also a decrease in the second variable"
This describes a positive linear relationship, not a negative one.
So, the correct answer is Option D -"There is a linear relationship in which, when there is an increase in one variable, there is a decrease in the second variable."
