Question 1 :
Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? In order to answer this question an analysis is conducted. Let we wish to explain depth (in kilometers) of the quake below the surface at the epicenterx by magnitude of an earthquake (on
the Richter scale). Data are as follows:
Subject: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Magnitude of earthquake: 3.9, 4.3, 3.3, 4.6, 3.9, 3.2, 3.4, 4.5, 5.1, 2.6
Depth of quake: 8.8, 10.0, 11.2, 9.5, 12.8, 3.9, 5.5, 7.1, 8.5, 7.9
Subject: 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
Magnitude of earthquake: 3.3, 3.0, 4.5, 2.9, 4.5, 2.8, 5.1, 4.7, 3.5, 2.2
Depth of quake: 5.3, 5.0, 6.5, 7.6, 10.0, 6, 2, 11, 11, 9
Answer the following question step by step by your hand writing and provide the formulas and calculations:
a) Calculate the least squares estimates of the slope and intercept, and write fitted simple linear regression model.
b) What is an estimate of the mean earthquake depth when the magnitude is 3.3?
c) What is residual when the magnitude is 3.3?
d) Test the significance of regression.
i. State the hypotheses.
ii. Calculate ANOVA table.
iii. State your rejection criterion.
iv. Interpret your result. Use α=0.05.