Question

1. The following data represents the heights of the old faithful geyser eruptions, the durations of the eruption and the interval between eruptions. The data is attached and an excel file is also included on canvas. The data is arranged in duration, interval and height

a) Use the paired data for durations and intervals after eruptions of the geyser. Is there significant linear correlation at the 0.05 significance level suggesting interval after an eruption is related to duration (use the r value approach)?

b) Use the paired data for heights of eruptions and intervals after eruptions of the old faithful geyser. Is there significant linear correlation suggesting interval is related to height? Use a 0.05 significance level and again use r value approach.

c) Using the paired data for durations (x) and intervals (y) after eruptions of the geyser, find a linear regression equation. What is the best predicted time before the next eruption if the previous eruption lasted 210 seconds?

Duration	Interval	Height	Duration	Interval	Height
240	86	140	120	57	139
237	86	154	267	100	110
122	62	140	103	62	140
267	104	140	270	87	135
113	62	160	241	70	140
258	95	140	239	88	135
232	79	150	233	82	140
105	62	150	238	83	139
276	94	160	102	56	100
248	79	155	271	81	105
243	86	125	127	74	130
241	85	136	275	102	135
214	86	140	140	61	131
114	58	155	264	83	135
272	89	130	134	73	153
227	79	125	268	97	155
237	83	125	124	67	140
238	82	139	270	90	150
203	84	125	249	84	153
270	82	140	237	82	120
218	78	140	235	81	138
226	91	135	228	78	135
250	89	141	265	89	145
245	79	140	120	69	130
241	79	150	275	98	136

Answer 1

1. The following data represents the heights of the old faithful geyser eruptions, the durations of the eruption and the interval between eruptions. The data is attached and an excel file is also included on canvas. The data is arranged in duration, interval and height

a) Use the paired data for durations and intervals after eruptions of the geyser. Is there significant linear correlation at the 0.05 significance level suggesting interval after an eruption is related to duration (use the r value approach)?

Calculated r=0.8701 which is > 0.279 the critical r at 0.05 level of significance. r is significant.

There is a significant linear correlation at the 0.05 significance level suggesting interval after an eruption is related to duration.

b) Use the paired data for heights of eruptions and intervals after eruptions of the old faithful geyser. Is there significant linear correlation suggesting interval is related to height? Use a 0.05 significance level and again use r value approach.

Calculated r=0.-0.0098

|r| = 0.0098 which is < 0.279 the critical r at 0.05 level of significance. r is not significant.

There is no significant linear correlation at the 0.05 significance level suggesting interval is related to height.

c) Using the paired data for durations (x) and intervals (y) after eruptions of the geyser, find a linear regression equation. What is the best predicted time before the next eruption if the previous eruption lasted 210 seconds?

The estimated regression line is

Interval (y) =41.945 +0.179 * durations (x)

When duration = 210,

Predicted Interval (y) =41.945 +0.179 * 210

=79.47

Excel Addon Megastat used.

Menu used: correlation/Regression ---- Correlation Matrix

Correlation Matrix
		Duration	Interval	Height
	Duration	1.0000	0.8701	-0.0187
	Interval	0.8701	1.0000	-0.0098
	Height	-0.0187	-0.0098	1.0000
		50	sample size
		± .279	critical value .05 (two-tail)
		± .361	critical value .01 (two-tail)

Menu used: correlation/Regression ---- Regression Analysis.

Regression Analysis
	r²	0.757	n	50
	r	0.870	k	1
	Std. Error of Estimate	5.964	Dep. Var.	Interval
Regression output						confidence interval
variables		coefficients	std. error	t (df=48)	p-value	95% lower	95% upper
Intercept	a =	41.945
Duration	b =	0.179	0.015	12.231	2.33E-16	0.149	0.208
ANOVA table
Source	SS	df	MS	F	p-value
Regression	5,321.685	1	5,321.685	149.60	2.33E-16
Residual	1,707.535	48	35.574
Total	7,029.220	49
Predicted values for: Interval
		95% Confidence Interval		95% Prediction Interval
Duration	Predicted	lower	upper	lower	upper	Leverage
210	79.47	77.77	81.18	67.36	91.59	0.020