Final answer:
The question pertains to determining whether a data set shows a positive correlation, negative correlation, or no correlation. A positive correlation occurs when both variables increase together, while a negative correlation occurs when one variable increases as the other decreases. Zero correlation means there is no discernible relationship between the variables. Option c is the correct answer.
Step-by-step explanation:
In analyzing data for the presence and direction of a correlation, we look for patterns or relationships between variables. When there is a positive correlation, we see that as one variable increases, so does the other, and this relationship is represented with a correlation coefficient (r) between 0 and 1. On the other hand, a negative correlation indicates that as one variable increases, the other decreases, shown as r values between -1 and 0. A particular instance of zero correlation, where r equals 0, would imply that there is no discernible relationship between the variables in question.
Looking at scatter plots can be helpful in visualizing these relationships. A scatter plot showing a line with a positive slope suggests a positive correlation, while a scatter plot with a line having a negative slope implies a negative correlation. In the absence of a slope, where data points do not suggest an increasing or decreasing relationship, one would recognize no correlation.
Regarding the correlation coefficient, it indicates the weakest relationship when it is closest to 0, which aligns with the idea of zero correlation. In addition to observing the scatter plots, the use of the least-squares line and calculation of the correlation coefficient serve as quantitative methods to assess the correlation's significance.
When discussing specific datasets, outlier points can distort the correlation. Decisions about including or excluding outliers depend on their impact and the context of the study. Overall, while correlation can reveal patterns between variables, it does not imply causation, and care should be taken not to misconstrue correlations as evidence of a causal link.