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

1.3

Use a significance level of

0.05

Mag   Depth
1.74   2.1
2.75   14.6
2.21   13.4
2.06   3.9
2.42   13.7
0.99   17.4
1.03   4.7
1.81   4.8
2.83   15.2
0.45   17.2
2.67   18.3
2.61   8.3
0.87   4.1
1.32   9.1
1.66   15.7
1.38   19.3
1.13   9.4
0.94   15.3
0.54   2.7
2.15   18.4
2.79   19.1
0.18   9.3
1.76   2.1
0.94   14.6
2.86   3.2
2.88   3.3
1.27   3.3
2.98   19.6
1.47   8.4
1.64   13.8
1.16   19.1
2.78   11.9
1.38   6.8
1.65   11.7
1.21   14.3
1.93   7.3
1.54   8.4
2.91   18.2
0.92   11.9
1.44   10.8
1.96   8.4
2.58   6.3
2.97   10.3
1.83   12.3
2.87   7.4
0.89   15.4
0.03   12.7
2.62   17.2
2.98   19.9
0.67   6.9

Answer 1

Applying regression on above data with data analysis tool of excel:

	Coefficients	Standard Error	t Stat	P-value
Intercept	9.5808	1.8336	5.2252	0.0000
Mag	0.9302	0.9371	0.9926	0.3259

since p value >0.05 level regression is not significant:

best predicted depth of an earthquake with a magnitude of 1.3 =average value of all depth

= 11.23