Question

s 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 3.2 4.2 3.3 4.5 2.6 3.2 3.4 y 4.9 9.9 11.2 10.0 7.9 3.9 5.5 (a) Make a scatter diagram of the data. Selection Tool Line Ray Segment Circle Vertical Parabola Horizontal Parabola Point No Solution Help 12345123456789101112 Clear Graph Delete Layer Fill WebAssign Graphing Tool Graph LayersToggle Open/Closed After you add an object to the graph you can use Graph Layers to view and edit its properties. Then visualize the line you think best fits the data. (b) Use a calculator to verify that Σx = 24.4, Σx2 = 87.58, Σy = 53.3, Σy2 = 455.33 and Σxy = 190.94. 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, y should tend to decrease as x increases. Given our value of r, y should tend to remain constant as x increases. Given our value of r, y should tend to increase as x increases. Given our value of r, we can not draw any conclusions for the behavior of y as x increases.

Answer 1

a)

b)

	X	Y	X^2	Y^2	XY
	3.2	4.9	10.24	24.01	15.68
	4.2	9.9	17.64	98.01	41.58
	3.3	11.2	10.89	125.44	36.96
	4.5	10	20.25	100	45
	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	18.7
SUM	24.4	53.3	87.58	455.33	190.94
n	7
Mean	3.485714	7.614285714
SSxx	2.528571	Sum(x^2) - ((Sum(x))^2 /n)	SSR	10.49494	slope * Ssxy	MSR	10.49494
Ssyy	49.48857	Sum(y^2) - ((Sum(y))^2 /n)	SSE	38.99363	SST-SSR	MSE	7.798725
Ssxy	5.151429	Sum(xy) - (Sum(x)*Sum(y)/n)	SST	49.48857	Ssyy	F	1.345726
slope	2.037288	Ssxy/SSxx
intercept	0.512881	Mean Y - Mean X * Slope
Se	2.79262	SQRT(SSE/(n-2))
Sb1	1.756201	Se/SQRT(SSxx)
r	0.460508	Ssxy/SQRT(SSxx*Ssyy)
r^2	0.212068

c)

r = 0.4605, Week relationship between X and Y variables and positive correlation

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