Which of the following values would not be a valid correlation coefficient?
1. 3
2. 0.04
3. 0.5
4. 0.7
Answer (1)
In mathematics, the correlation coefficient is a numerical measure that quantifies the strength and direction of a linear relationship between two variables. The correlation coefficient, usually denoted as r , can range between -1 and 1 . Here is what these values signify:
r = 1 : Perfect positive correlation, indicating that as one variable increases, the other variable also increases perfectly in a linear manner.
r = -1 : Perfect negative correlation, meaning that as one variable increases, the other decreases perfectly in a linear manner.
r = 0 : No correlation, which indicates there is no linear relationship between the variables.
For any correlation coefficient to be valid, it must fall within this range of -1 to 1 .
Now, let's evaluate the given options:
3.2 : This value is outside the valid range of -1 to 1 , so it would not be a valid correlation coefficient.
0.04 : This is a valid correlation coefficient as it lies within the range of -1 to 1 .
0.5 : This is also a valid correlation coefficient, falling within the acceptable range.
0.7 : This is a valid correlation coefficient for the same reason as above.
From the given options, the value that would not be a valid correlation coefficient is 3.2 .
