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 1.9. Use a significance level of 0.05 mamns ran Click the icon to view the earthquake measurements on coefficient r The regression equation is y Round to one decimal place as needed) km. Given that the earthquake has a magnitude of 1.9, the best predicted depth is (Round to one decimal place as needed)

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Depth
Independent Variable: Mag
Depth = 12.809263 - 0.91935145 Mag
Sample size: 50
R (correlation coefficient) = -0.13581435
R-sq = 0.018445538
Estimate of error standard deviation: 5.4009443

Parameter estimates:

Analysis of variance table for regression model:

Hence,

Regression equation is:

y = 12.8 + (-0.9) x

Predicted depth is 11.5 km

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 12.809263 1.6148193 0 48 7.9323195 <0.0001 Slope -0.91935145 0.96799359 0 48 -0.94974952 0.347

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