The table below lists measurements from eight different eruptions of the Old Faithful geyser in Yellowstone National Park. The data consist of the duration (sec) of the eruption, height (ft) of the eruption, time interval (min) before the eruption, and time interval (min) after the eruption. Shown below are Minitab results obtained by using the durations and interval-after times.
a. Determine whether there is sufficient evidence to support a claim of a linear correlation between duration and interval-after time for eruptions of the Old Faithful geyser.
b. What percentage of the variation in interval-after times can be explained by the linear correlation between interval-after times and durations?
c. Letting y represent interval-after time and letting x represent duration time, identify the regression equation.
d. If an eruption has duration of 200 sec, what is the best predicted value for the time interval after the eruption to the next eruption?

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Eruptions of the Old Faithful Geyser Duration Height Interval Before Interval After 240 140 98 92 120 178234 235 269 255220 140 93 83 110 90 65 125 92 72 120 98 94 120 105 94 125 81 101 150 108 87 Pearson correlation of DURATION and AFTER0.926 value- 0 . 001 The regression equation is AFTER 34.8 ◆ 0.234 DURATION