To estimate the correlation coefficient based on the data provided, let's first analyze the values:
The data points given in the table are:
- (0, 3)
- (2, 6)
- (4, 9)
- (6, 12)
- (8, 15)
- (10, 18)
By plotting these points on a scatter plot, we would observe that as the 'x' values increase (0, 2, 4, 6, 8, 10), the corresponding 'y' values also increase (3, 6, 9, 12, 15, 18). This indicates a positive linear relationship between 'x' and 'y'.
Now, estimating the correlation coefficient, which ranges from -1 to 1:
- A value of +1 indicates a perfect positive linear relationship.
- A value of 0 indicates no linear relationship.
- A value of -1 indicates a perfect negative linear relationship.
Since the points appear to form a straight line with a positive slope, we can estimate that the correlation coefficient is quite high. Given the options:
- 0.9
- −0.9
- 1
- −1
The closest estimation based on the strong positive correlation observed is:
1 (indicating a perfect positive linear relationship).
So, the best estimated answer would be 1.
1 answer