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 1.5 Use a significance level of 0.05.

Mag   Depth
0.74   5.3
0.84   12.1
0.36   2.4
1.15   7.7
2.23   18.9
1.67   15.5
0.49   10.4
2.67   16.5
2.67   2.4
1.96   5.3
1.14   3.9
1.64   6.9
0.94   14.2
1.23   6.3
0.05   16.8
2.31   18.6
0.84   17.7
0.94   17.3
1.51   11.6
0.19   13.1
2.14   14.4
0.29   11.1
0.36   9.2
1.33   9.1
2.99   19.8
0.27   2.4
1.08   7.4
2.61   3.8
2.12   5.2
1.64   5.5
0.33   18.7
2.62   7.5
0.22   2.9
1.23   3.7
0.73   7.4
0.28   8.2
1.28   9.7
2.35   13.2
2.65   15.7
1.13   14.5
0.63   12.1
2.08   3.9
2.18   11.6
0.32   10.2
0.02   7.1
0.21   3.5
0.17   5.6
2.32   5.7
1.58   6.3
1.05   18.3

The regression equation is ^y = ? + ? x

​(Round to one decimal place as​ needed.)

Given that the earthquake has a magnitude of
1.5​, the best predicted depth is ?

​(Round to one decimal place as​ needed.)

Answer 1

from excel: data -data analysis: regression:

	df	SS	MS	F	Significance F
Regression	1	27.66559	27.66559	0.990117	0.324704
Residual	48	1341.203	27.94173
Total	49	1368.869
	Coefficients	Standard Error	t Stat	P-value
Intercept	8.829802	1.336339	6.607457	2.94E-08
Mag	0.864063	0.868364	0.995046	0.324704

1)

regression equation y^ =8.8+0.9x

2)

since p value >0.05 regression is not significant

the best predicted depth is =average value of depth = 9.9