Final answer:
If the correlation between two variables is zero, it means there is no relationship between them in a linear sense. In the context of the question, the score on a test is not affected by whether or not breakfast had been eaten.
Step-by-step explanation:
The correlation being zero in this case suggests that there is no relationship between eating breakfast and test performance. That is, the behavior of one variable cannot be predicted from the other. This doesn't imply that they cannot be connected in some other manner; only not in a linear one. In simple terms, whether a student eats breakfast or not does not impact the test performance. The zero-correlation scenario is depicted in Figure 12.10 (c) where the scatter plot shows data with zero correlation: r=0.
Let's further elaborate this with a correlation explanation. Correlation is a statistical technique used to determine the degree to which two variables are related. It measures both the strength and direction of the linear relationship between two variables. A positive correlation indicates that as one variable increases, the other does too, while a negative correlation indicates that as one variable increases, the other decreases. When the correlation is 0, it means that there is no linear relationship between the two variables, implying that they do not influence each other.
Learn more about Correlation