Question

1. Old Faithful, located in Yellowstone National Park, is the world’s most famous geyser. The durations (in minutes) of several of Old Faithful’s eruptions and the times (in minutes) until the next eruption are shown in the table below. Calculate the correlation coefficient and determine the “best fit” line equation using linear regression.

x (duration)	y (time)	x (duration)	y (time)
1.8	56	3.78	79
1.82	58	3.83	85
1.90	62	3.88	80
1.93	56	4.10	89
1.98	57	4.27	90
2.05	57	4.30	89
2.13	60	4.43	89
2.30	57	4.47	86
2.37	61	4.53	89
2.82	73	4.55	86
3.13	76	4.60	92
3.27	77	4.63	91
3.65	77

2. Using the equation for the best-fit line from problem 1, determine the following:

1. If the duration of an eruption of Old Faithful is 2.90 minutes, how long until it erupts again?
2. If the time between eruptions is 65 minutes, how long will the eruption last?

3. The US navy has done a lot of research on the optimal time for a scuba diver to be on the bottom of the ocean. The Navy defines the optimal time to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x = depth of dive in meters and y = optimal time in hours. A random sample of divers gave the following data (based on information taken from Medical Physiology by A. C. Guyton, M.D.)

x	14.1	24.3	30.2	38.3	51.3	20.5	22.7
y	2.58	2.08	1.58	1.03	0.75	2.38	2.20

Use a 1% level of significance to test the claim that ρ < 0. (I do need you to step through the five steps of hypothesis testing that we have been using in class. You can use SPSS to calculate r and as a check to what you find when you complete the hypothesis test).

Answer 1

Hi, We are supposed to answer one question at a time.Since you have not mentioned which question to answer, I am answering the first one. Kindly repost the question with another question you would like to be answered

1.

To find the best fit equation, following steps need to be taken

Step 1: Just put the data in the excel spreadsheet

Step 2: Go to Data --> Data Analysis --> regression --> select the data

Step 3: Get the regression output

The best fit line equation is :

x = -2.445 + 0.0767y

A) if the duration is 2.90 minutes, the time will be :

B) It time is 65 minutes, the duration will be: