Answer:
C) r = 0.417
Step-by-step explanation:
The product moment correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It tells us how closely the data points in a scatter plot cluster around a straight line.
The PMCC is always between +1 and -1:
- r = 1 indicates a perfect positive correlation (all data points fall exactly on a straight line with a positive slope).
- r = -1 indicates a perfect negative correlation (all data points fall exactly on a straight line with a negative slope).
- r = 0 indicates no linear correlation between the variables.
In the given scatter plot, the line of best fit has a positive slope. This indicates a positive correlation, and so the r-value is positive.
A correlation coefficient of r = 0.826 indicates a strong positive correlation between the two variables. The data points would form a clear, upward-sloping pattern on a scatter plot, and they would cluster closely around a straight line.
As the data points are not tightly clustered around the line of best fit, but still show a discernible trend, it indicates a moderate strength of correlation. Therefore, the correlation coefficient that matches the given scatter plot is r = 0.417.
