Question

A data set is provided, entitled oldfaithful_asst, on the duration and height of the Old Faithful geyser in the Yellowstone National Park.

1. Construct a scatterplot using Excel or any software (SPSS or Minitab) between the variables “duration” and “height.” Please title the graph “Scatterplot 1 Old Faithful” and create labels for both axes.
2. There seems to be a an outlier in the data set. Although an outlier is not a detriment to the data analysis, as part of an exercise, identify the outlier and delete it (simply erase its value, do not replace with zero).

• Show the new (second) scatterplot and title the graph “Scatterplot 2 Old Faithful”
• Describe the pattern that emerges. What might this relationship imply?

3. Compute the correlation coefficient between the two variables and interpret this correlation. Refer to both the strength and direction of the correlation in your interpretation. Also interpret the correlation in terms of r-squared (coefficient of determination).
4. Conduct a regression to predict duration of an eruption using height and interpret the sample slope coefficient in words.
5. What is the predicted duration for an eruption that is 115?

Old Faithful data set to answer problem:

Duration	Height
240	140
237	140
250	148
243	130
255	125
120	110
260	136
178	125
259	115
245	120
234	120
213	120
255	150
235	140
250	136
110	120
245	148
269	130
251	130
234	136
252	130
254	115
273	136
266	130
284	138
252	120
269	120
250	120
261	95
253	140
255	125
280	130
270	130
241	110
272	110
294	125
440	250
220	150
253	130
245	120
274	95

Answer 1

a)

b)

Firstly the data point (440,250) was removed as an outlier.

There are no such significant changes in the variable duration as the variable height increases.

This pattern indicates there is no such linear dependence between these two variables.

c)

Pearson correlation of Duration and Height = 0.092
The correlation indicates there is a very weak positive linear dependence between the two variables.

The r² = 0.008464

In terms of the coefficient of determination, we can say that only 0.84% of the variability of Duration is getting explained by Height.

d)

The regression equation is given by

Duration = 212.8 + 0.253 Height

The slope coefficient is 0.253 and can be interpreted as the amount of increase in Duration due to a unit increase in Height.

f)

The predicted value of Duration when Height = 115, is 212.8 + 0.253*115 = 241.895.

PLEASE LEAVE AN UPVOTE!!