Question

Cardiologists use the short-range scaling exponent 09, which measures the randomness of heart rate patterns, as a tool to assess risk of heart attack. The article "Applying Fractal Analysis to Short Sets of Heart Rate Variability Data" compared values of a computed from long series of measurements (approximately 40,000 heartbeats) with those estimated from the first 300 beats to determine how well the long-term measurement (y could be predicted the short-term one (x). Following are the data obtained by digitizing a graph). short 0.5 1.02 1.4 Long 0.65 0.79 0.81 0.88 1.68 1.16 1.05 1.05 1.05 0.82 0.93 1.07 1.26 1.1 1.19 1.18 0.81 1.19 0.81 1.28 1.18 0.71 1.2 1.23 1.23 1.24 Note: This problem has a reduced data set for ease of performing the calculations required. This differs from the data set given for this problem in the text. Find a 95% confidence Interval for the mean long-term measurement for those with short-term measurements of 1.2. Round the answers to three decimal places. The 95% confidence Interval is (0.936

Answer 1

Applying regression from Megastat on above data:

Regression output					confidence interval
variables	coefficients	std. error	t (df=13)	p-value	95% lower	95% upper
Intercept	0.9483	0.1792	5.290	.0001	0.5610	1.3355
x	0.0977	0.1657	0.590	.5655	-0.2602	0.4556
Predicted values for: y
		95% Confidence Interval		95% Prediction Interval
x	Predicted	lower	upper	lower	upper	Leverage
1.2	1.06550	0.94611	1.18490	0.64158	1.48943	0.086

1)

95% confidence interval = (0.946 , 1.185)

2)

95% prediction interval = (0.642 , 1.489)