Solution ?3 RE Old Faithful? Refer to the table of data given in Exercise 1 and use the durations and heights. a.? Construct a scatterplot. What does the scatterplot suggest about a linear correlation between duration and height? b.? Find the value of the linear correlation coefficient and determine whether there is sufficient evidence to support a claim of a linear correlation between duration and height. c.? Letting ?y? represent height and letting ?x? represent duration, find the regression equation. d.? If an eruption has a duration of 200 sec, what is its best predicted height? Exercise 1 Old Faithful? 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 a duration of 200 sec, what is the best predicted value for the time interval after the eruption to the next eruption? Eruptions of the Old Faithful Geyser D u r a t i o n H e i g h t I n t e r v a l B e f o r e I n t e r v a l A f t e r
Solution 3 RE Step 1 : Given, In a Yellow stone park eight different eruptions of the old faithful geyser which consists of duration and height of the eruption, the time interval has been recorded before and after the eruption. Following are the steps to analyze correlation and regression from Stat Disk . Enter the dataset in stat disk AnalysisCorrelation and regression. . Choose level of significance evaluate . After obtaining the results click ok on Scatter plot. The Scatter plot for the given data is We can see that the points are are not showing any pattern, points are scattered around the line. So, we can say that the plot is not linear Step 2 : The correlation and regression for the given data is The correlation r = 0.3894 and critical value is ±0.7067. Since, the value of r lies in critical value so we can conclude that there is no correlation between the variables. The P-Value 0.3402 which is greater than the level of significance. Hence, there is no correlation between the variables heights and interval after eruptions.