Question

Fifty matched pairs of​ magnitude/depth measurements randomly selected from​ 10,594 earthquakes recorded in one year from a location in southern California. Find the best predicted depth of an earthquake with a magnitude of 1.6. Use a significance level of 0.05

Mag	Depth
0.56	14.5
1.42	17.6
1.37	14.3
1.33	10.8
0.18	15.9
1.54	16.3
0.96	11.1
1.93	11.9
0.82	15.1
0.97	2.7
0.84	4.7
0.46	12.8
1.04	11.4
2.54	12.1
0.76	18.8
1.76	17.5
0.81	18.3
1.74	2.1
0.96	2.4
2.38	11.7
2.91	15.8
2.68	16.2
0.99	7.5
0.79	17.7
0.03	6.7
2.31	4.74
2.74	17.9
0.71	18.9
0.52	14.1
1.91	3.1
2.27	3.7
1.77	2.6
1.24	3.1
2.95	15.2
1.04	10.9
1.75	12.3
0.74	10.5
0.13	10.1
2.96	11.7
0.02	14.2
1.98	6.6
0.06	19.4
0.21	11.2
0.34	9.6
0.39	11.8
2.48	11.9
0.72	5.5
0.52	19.4
0.23	5.1
1.82	3.2

The regression equation is?

The best prediction is y overbar​,the mean depth. Determine the mean depth​, rounding to three decimal places.

Answer 1

The statistical software output for this problem is:

From above output:

a) Regression equation:

y = 11.746 - 0.388 x

b) The correlation is not significant. So,

Best predicted value = Mean of y values = 11.253