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. x 3.4 4.0 3.3 4.5 2.6 3.2 3.4 y 5.5 10.0 11.2 10.0 7.9 3.9 5.5 (a) Make a scatter diagram of the data. Then visualize the line you think best fits the data. (b) Use a calculator to verify that Σx = 24.4, Σx2 = 87.26, Σy = 54.0, Σy2 = 463.56 and Σxy = 192.38. Compute r. (Round to 3 decimal places.) As x increases, does the value of r imply that y should tend to increase or decrease? Explain your answer. Given our value of r, we can not draw any conclusions for the behavior of y as x increases. Given our value of r, y should tend to decrease as x increases. Given our value of r, y should tend to increase as x increases. Given our value of r, y should tend to remain constant as x increases.

Answer 1

Solution

Part (a): Scatter

12
							•
10								•	•
8							•
						•
6
						•	•
4
2
0
	0.5	1.0	1.5	2.0	2.5	3.0	3.5	4.0	4.5	5.0

Answer 1

Part (b)

x	y	x^2	y^2	xy
3.4	5.5	11.56	30.25	18.70
4.0	10.0	16.00	100.00	40.00
3.3	11.2	10.89	125.44	36.96
4.5	10.0	20.25	100.00	45.00
2.6	7.9	6.76	62.41	20.54
3.2	3.9	10.24	15.21	12.48
3.4	5.5	11.56	30.25	18.70
24.4	54.0	87.26	463.56	192.38

All the given figures tally. Answer 2

Correlation coefficient, r = Sxy/sqrt(Sxx. Syy) = 0.4075 Answer 3

where

Mean X = Xbar = (1/n) Σ(i = 1 to n)x_i = 3.4857;

Mean Y = Ybar = (1/n) Σ(i = 1 to n)y =7.7143_i

Sxx = Σ(i = 1 to n)(x_i – Xbar)² = 2.208571429;

Syy = Σ(i = 1 to n)(y_i – Ybar) ² = 46.98857143;

Sxy = Σ(i = 1 to n){(x_i – Xbar)(y_i – Ybar)} = 4.151428571

Given our value of r, y should tend to increase as x increases. Answer 4

[Because r is positive]

DONE