in which of the following do you expect the correlation coefficient to be closest to 1?
in which of the following do you expect the correlation coefficient to be closest to 1?
Answer
Explanation:
Step1: Recall correlation - coefficient concept
The correlation coefficient $r$ measures the strength and direction of a linear relationship. A value of $r = 1$ indicates a perfect positive - linear relationship.
Step2: Examine scatter - plots for linearity
We need to look for a scatter - plot where the points lie close to a straight line with a positive slope.
Step3: Analyze the given scatter - plot
In a scatter - plot with a correlation coefficient close to 1, the points should show a clear upward trend and be clustered closely around a straight line. Without seeing the second scatter - plot (since only one is fully visible in the image), if the other scatter - plots have more scattered points or non - linear trends, the scatter - plot with points that seem to follow an upward linear path most closely will have a correlation coefficient closest to 1.
Answer:
The scatter - plot where the points form a tight upward - sloping linear pattern. Since only one full scatter - plot is shown, if it has the most linear and upward - sloping pattern compared to the non - shown ones, it is the answer.