Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? Let x be the magnitude of an earthquake (on the Richter scale), and let y be the depth (in kilometers) of the quake below the surface at the epicenter. Suppose a random sample of earthquakes gave the following information.
As x increases, does the value of r imply that y should tend to increase, decrease, or remain the same? Explain.
Since r is zero, as x increases, y decreases.
Since r is negative, as x increases, y remains the same.
Since r is negative, as x increases, y decreases.
Since r is positive, as x increases, y increases.
Since r is positive, as x increases, y remains the same.
I think it is D
Information missing, so I cannot help with the first part.
Positive correlation indicates that both variables increase and decrease together. A negative correlation indicates one variable increases while the other increases. Thus both the third and fourth choice are correct.
To determine the relationship between the magnitude of an earthquake (x) and the depth below the surface (y), we need to interpret the correlation coefficient (r).
The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation.
In this case, if the correlation coefficient (r) is negative, it indicates a negative correlation between x and y. This means that as x increases, the value of y tends to decrease. Therefore, the correct answer is "Since r is negative, as x increases, y decreases" (choice C).
It is important to note that this conclusion is based on the assumption that the correlation coefficient is the only factor considered in determining the relationship between x and y. Other factors, such as the specific geological characteristics of the region, should also be taken into account for a comprehensive understanding of the relationship between earthquake magnitude and depth.