Question

3. Data for magnitude and longitude for a sample of 24 earthquakes are below. The objective is to determine whether the magnitude of an earthquake is associated (predicted) by its longitude coordinates.

Longitude	Magnitude
-118.85	2.54
-122.20	2.9
-119.80	2.81
-104.82	3.5
-115.09	3.4
-97.15	3.2
-122.81	2.5
-121.75	2.7
-114.96	3.4
-115.54	3.2
-70.60	3.8
-113.4	2.8
-117.73	2.9
-117.66	2.8
-115.76	2.9
-116.46	2.8
-115.27	2.6
-115.14	2.6
-115.77	3.3
-121.49	3.1
-104.97	2.8
-121.02	2.8
-115.08	3.4
-122.19	2.8

  

3a. Specify the null and alternative hypotheses regarding model fit (1 point)

3b. Calculate the test statistic for model fit (3 points) and state your conclusion using an alpha of 5% (1 point)

Let’s compare the results you calculated for Q3b with results from a multiple linear regression.

4a. Would additionally controlling for ‘depth’ and ‘latitude’ be helpful? In other words, is a model that includes ‘depth’, ‘latitude’ and ‘longitude’ superior in model fit to a model that includes only ‘longitude’? Output for a multiple linear regression which includes longitude, depth, and latitude is provided below. (2 points)

4b. Interpret the parameter estimate for ‘longitude’ from the multiple linear regression output. (1 point)

Analysis of Variance
Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	3	1.07870	0.35957	4.38	0.0159
Error	20	1.64090	0.08204
Corrected Total	23	2.71960

Root MSE	0.27953	R-Square	0.3966
Dependent Mean	2.98200	Adj R-Sq	0.3104
Coeff Var	9.37398

Parameter Estimates
Variable	DF	Parameter Estimate	Standard Error	t Value	Pr > |t|
Intercept	1	4.86602	0.85582	5.69	<.0001
Depth	1	0.00131	0.01084	0.12	0.9049
Latitude	1	0.00564	0.01108	0.51	0.6157
Longitude	1	0.01849	0.00561	3.29	0.0035

Answer 1

3a)

3b)

4)