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. Would you say the correlation is low, moderate, or strong? Positive or negative? If necessary, draw a scatter diagram of the given data.
$$\begin{array} { c | c c c c c }
\hline x & 2.5 & 4 & 3.4 & 4.4 & 2.4 \
\hline y & 5.2 & 10.3 & 10.8 & 10.3 & 8.3 \
\hline
\end{array}$$
A)moderate and positive
B)moderate and negative
C)low and positive
D)strong and positive
E)strong and negative

Question

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. Would you say the correlation is low, moderate, or strong? Positive or negative? If necessary, draw a scatter diagram of the given data.
$$\begin{array} { c | c c c c c } 
\hline x & 2.5 & 4 & 3.4 & 4.4 & 2.4 \
\hline y & 5.2 & 10.3 & 10.8 & 10.3 & 8.3 \
\hline
\end{array}$$
A)moderate and positive
B)moderate and negative
C)low and positive
D)strong and positive
E)strong and negative

Quizplus · Accepted Answer

The correlation is positive because as the magnitude of the earthquake increases, the depth of the quake below the surface also tends to increase. The correlation is moderate because the points are scattered around the line of best fit, but there is a general trend.

Is the Magnitude of an Earthquake Related to the Depth x2.543.44.42.4y5.210.310.810.38.3\begin{array} { c | c c c c c } \hline x & 2.5 & 4 & 3.4 & 4.4 & 2.4 \\\hline y & 5.2 & 10.3 & 10.8 & 10.3 & 8.3 \\\hline\end{array}xy​2.55.2​410.3​3.410.8​4.410.3​2.48.3​​

Is the Magnitude of an Earthquake Related to the Depth $\begin{array} { c | c c c c c } \hline x & 2.5 & 4 & 3.4 & 4.4 & 2.4 \\\hline y & 5.2 & 10.3 & 10.8 & 10.3 & 8.3 \\\hline\end{array}$