Fifty matched pairs of magnitude/depth measurements randomly selected from 10,59

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 1.1. Use a significance level of 0.05.

1.The regression equation is _______

2. Best predicted depth is ___ km

DATA-

Mag Depth

2.02 2.4

2.74 15.7

1.91 4.7

2.32 17.6

1.69 7.5

0.67 8.1

0.93 5.1

1.16 10.8

1.73 5.4

2.79 12.8

2.36 13.6

2.84 16.9

2.95 14.5

2.48 11.9

1.44 13.5

1.83 5.9

2.78 12.2

1.28 17.3

2.82 9.1

2.63 2.8

0.95 3.4

1.86 16.3

2.16 15.7

1.56 5.5

0.88 14.9

1.48 14.8

1.24 9.8

1.09 4.1

2.45 11.3

2.34 10.7

2.75 12.2

1.83 4.8

2.04 12.8

1.47 7.5

0.92 18.7

2.23 13.1

0.89 4.6

0.15 15.6

0.24 5.5

1.34 16.3

0.06 9.5

0.05 3.4

2.17 3.2

2.68 6.9

0.16 11.9

0.58 8.9

0.77 14.4

0.81 9.6

2.19 17.3

2.69 19.4

Explanation / Answer

Here dependent variable is depth and independent variable is magnitude.

First we have to find regression equation.

We can find regression equation using EXCEL.

steps :

ENTER data into EXCEL sheet --> Data ->Data analysis --> Regression --> ok --> Input Y range : selet range of depth --> Input X range : select range of mag --> Click on labels --> Output Range : Select one empty cell --> ok

From the given output the regression equation is,

depth = 8.55 + 1.23*mag

Find the best predicted depth of an earthquake with a magnitude of 1.1.

Here we have to find depth when mag = 1.1

This we can find using regression equation.

depth = 8.55 + 1.23*1.1

depth = 9.90

Also we can see than model is insignificant since p-value for the model is 0.136 which is greator than 0.05.

Magnitude is insignificant variable.

SUMMARY OUTPUT Regression Statistics Multiple R 0.213621359 R Square 0.045634085 Adjusted R Square 0.025751462 Standard Error 4.850782049 Observations 50 ANOVA df SS MS F Significance F Regression 1 54.00564871 54.00564871 2.295174 0.136334616 Residual 48 1129.444151 23.53008649 Total 49 1183.4498 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 8.550406429 1.515691648 5.641257205 8.81E-07 5.50290412 11.59790874 5.50290412 11.59790874 mag 1.227574083 0.81028888 1.514983252 0.136335 -0.401620903 2.85676907 -0.401620903 2.85676907

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