Final answer:
The amount of variability in GPA explained by GRE scores is 36%, which is obtained by squaring the correlation coefficient (r^2 = 0.60^2 = 0.36). The question's options do not include the correct value, but the closest provided option is B) 0.30, which does not match the accurate calculation.
Step-by-step explanation:
In attempting to understand the relationship between GRE scores and GPA upon graduation, it's important to consider the correlation coefficient provided, which is 0.60. This value indicates a moderate to strong positive relationship between the two variables. However, when asked about the amount of variability between GPA and GRE scores this correlation accounts for, we turn to the coefficient of determination, which is the square of the correlation coefficient (r^2).
To find the coefficient of determination, we square the correlation coefficient:
r^2 = (0.60)^2 = 0.36
This result informs us that 36% of the variability in GPA can be explained by GRE scores. Consequently, the variability in GPA that is not explained by GRE scores is 1 - 0.36 = 0.64 or 64%. This question often confuses students because it mixes up the concepts of correlation coefficient and the coefficient of determination. In this particular case, the correct option that represents the amount of variability is not listed since the question may refer to either the explained or unexplained variability. If we consider the unexplained variability, it should be around 0.64 or 64%, but if the question pertains to the explained variability, then it's approximately 0.36 or 36%.
If we are addressing the amount of variability explained by the GRE scores with the options provided, the closest percentage represented as a decimal would be option B) 0.30, but please note this is not the exact figure and the correct answer should be 0.36 if accurately calculated.