Correlation analysis of Geyser Data

Refer to the data in the table that was provided by a geologist and the National Park Service obtained at Old Faithful geyser at Yellowstone National Park. The duration values are times (in seconds) of an eruption, the interval values are times (in minutes) to the next eruption, and the height values are heights (in feet) of the eruptions.

Duration Interval Height
240 86 140
237 86 154
122 62 140
267 104 140
113 62 160
258 95 140
232 79 150
105 62 150
276 94 160
248 79 155
243 86 125
241 85 136
214 86 140
114 58 155
272 89 130

a) After each eruption, rangers at Old Faithful provide an estimate of the interval value, which is the time before the next eruption of Old Faithful. Construct a scatter diagram that uses the given values of interval and duration. Based on the result, does there appear to be a correlation between interval and duration?

b) Construct a scatter diagram that uses the given values of interval and height. Based on the result, does there appear to be a correlation between interval and height?

Table 1.2 Table for assessing the statistical significance of correlations

Number of data points Correlation coefficient required for significance at the 0.05 level Correlation coefficient required for significance at the 0.01 level
4 .950 .999
5 .878 .959
6 .811 .917
7 .754 .875
8 .707 .834
9 .666 .798
10 .632 .765
15 .514 .641
20 .444 .561
30 .361 .463
40 .312 .402
50 .279 .361
100 .196 .256

c) Computed value of the correlation coefficient is 0.933 for the interval/duration data. Refer to table 1.2 and interpret that result. What do you conclude about the significance of the correlation between interval and duration? What percent of the variation in interval can be explained by the variation in duration?

d) Computed value of the correlation coefficient is -0.382 for the interval/height data. Refer to table 1.2 and interpret that result. What do you conclude about the significance of the correlation between interval and height? What percent of the variation in interval can be explained by the variation in height?

See attached file for full problem description.