Old Faithful, the most reliable geyser in Yellowstone National Park can shoot up to 8,400 gallons of boiling water to a height of about 150 feet. More than 1,000,000 eruptions have been recorded. There is evidence that eruptions of Old Faithful can best be predicted by knowing the duration of the previous eruption. The results from regression analysis of Waiting Time (minutes) between eruptions versus Duration (minutes) of the previous eruption for a random sample of 222 eruptions are shown below. Waiting Time 95 Statistic Duration WaitingTime Mean 3.576 71.009 75 Standard Deviation 1.084 12.799 55 Sample Size 222 35 Correlation 0.877 1.5 2.5 3.5 Duration 4.5 5.5 Slope 10.358 Intercept 33.967 Predictor Coef SE Coef T P Intercept 33.967 1.428 23.79 0.0000 Duration 10.358 0.382 27.10 0.0000 Predicted Values for New Observations Duration Fit 4 75.4 SE Fit 0.444 95% CI 95% PI (74.5, 76.3) (63.2, 87.6) 1. At the 0.05 level of significance, is there evidence of a linear relationship between Duration and Waiting Time? Ho: Ha: Test statistic = P-value = Decision: Reject Ho Do not reject Ho Why you made this decision: Conclusion: There is not enough weak moderate strong overwhelming (choose one) statistical evidence of a linear relationship between Duration and Waiting Time. 2. Calculate and interpret the coefficient of determination. Coefficient of determination = Interpretation: 3. What is the equation of the fitted line? 4. Fill in the blanks in the following interpretation of the slope of the fitted line. As the duration of the previous eruption increases by the waiting time between eruptions increases by about minute(s), minutes on average. 5. If you just witnessed an eruption that lasted 4 minutes, how long do you predict you'll have to wait to see the next eruption? Predicted waiting time = minutes 6. So, you waited, and the next eruption came in 79 minutes. Is this an unusually long waiting time? Unusually long waiting time: Yes No Explanation:
Old Faithful, the most reliable geyser in Yellowstone National Park can shoot up to 8,400 gallons of boiling water to a height of about 150 feet. More than 1,000,000 eruptions have been recorded. There is evidence that eruptions of Old Faithful can best be predicted by knowing the duration of the previous eruption. The results from regression analysis of Waiting Time (minutes) between eruptions versus Duration (minutes) of the previous eruption for a random sample of 222 eruptions are shown below. Waiting Time 95 Statistic Duration WaitingTime Mean 3.576 71.009 75 Standard Deviation 1.084 12.799 55 Sample Size 222 35 Correlation 0.877 1.5 2.5 3.5 Duration 4.5 5.5 Slope 10.358 Intercept 33.967 Predictor Coef SE Coef T P Intercept 33.967 1.428 23.79 0.0000 Duration 10.358 0.382 27.10 0.0000 Predicted Values for New Observations Duration Fit 4 75.4 SE Fit 0.444 95% CI 95% PI (74.5, 76.3) (63.2, 87.6) 1. At the 0.05 level of significance, is there evidence of a linear relationship between Duration and Waiting Time? Ho: Ha: Test statistic = P-value = Decision: Reject Ho Do not reject Ho Why you made this decision: Conclusion: There is not enough weak moderate strong overwhelming (choose one) statistical evidence of a linear relationship between Duration and Waiting Time. 2. Calculate and interpret the coefficient of determination. Coefficient of determination = Interpretation: 3. What is the equation of the fitted line? 4. Fill in the blanks in the following interpretation of the slope of the fitted line. As the duration of the previous eruption increases by the waiting time between eruptions increases by about minute(s), minutes on average. 5. If you just witnessed an eruption that lasted 4 minutes, how long do you predict you'll have to wait to see the next eruption? Predicted waiting time = minutes 6. So, you waited, and the next eruption came in 79 minutes. Is this an unusually long waiting time? Unusually long waiting time: Yes No Explanation:
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Old Faithful, the most reliable geyser in Yellowstone National Park can shoot up to 8,400
gallons of boiling water to a height of about 150 feet. More than 1,000,000 eruptions have been
recorded.
There is evidence that eruptions of Old Faithful can best be predicted by knowing the duration of
the previous eruption. The results from regression analysis of Waiting Time (minutes) between
eruptions versus Duration (minutes) of the previous eruption for a random sample of 222
eruptions are shown below.
Waiting Time
95
Statistic
Duration WaitingTime
Mean
3.576
71.009
75
Standard Deviation
1.084
12.799
55
Sample Size
222
35
Correlation
0.877
1.5
2.5
3.5
Duration
4.5
5.5
Slope
10.358
Intercept
33.967
Predictor
Coef
SE Coef
T
P
Intercept
33.967
1.428
23.79
0.0000
Duration
10.358
0.382
27.10
0.0000
Predicted Values for New Observations
Duration Fit
4
75.4
SE Fit
0.444
95% CI
95% PI
(74.5, 76.3)
(63.2, 87.6)
1. At the 0.05 level of significance, is there evidence of a linear relationship between Duration
and Waiting Time?
Ho:
Ha:
Test statistic =
P-value =
Decision:
Reject Ho
Do not reject Ho
Why you made this decision:
Conclusion: There is not enough weak
moderate
strong
overwhelming (choose one)
statistical evidence of a linear relationship between Duration and Waiting Time.
Transcribed Image Text:2. Calculate and interpret the coefficient of determination.
Coefficient of determination =
Interpretation:
3. What is the equation of the fitted line?
4. Fill in the blanks in the following interpretation of the slope of the fitted line.
As the duration of the previous eruption increases by
the waiting time between eruptions increases by about
minute(s),
minutes on average.
5. If you just witnessed an eruption that lasted 4 minutes, how long do you predict you'll have to
wait to see the next eruption?
Predicted waiting time =
minutes
6. So, you waited, and the next eruption came in 79 minutes. Is this an unusually long waiting time?
Unusually long waiting time:
Yes
No
Explanation:
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