Question

The following sample observations were randomly selected. (Do not round the intermediate values. Negative amount should be indicated by a minus sign. Round your answers to 3 decimal places.)

X:	6	5	3	6	9
Y:	4	6	5	1	12

  

1. Determine the 0.99 confidence interval for the mean predicted when x = 6.

2. Determine the 0.99 prediction interval for an individual predicted when x = 6.

Answer 1

using excel>Addin>phstat>multiple sample test >Regression

we have

Simple Linear Regression Analysis
Regression Statistics
Multiple R	0.5884
R Square	0.3462
Adjusted R Square	0.1283
Standard Error	3.7695
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	22.5723	22.5723	1.5886	0.2966
Residual	3	42.6277	14.2092
Total	4	65.2000
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-0.7553	5.3167	-0.1421	0.8960	-17.6754	16.1648
x	1.0957	0.8694	1.2604	0.2966	-1.6710	3.8625

Confidence Interval Estimate
Data
X Value	6
Confidence Level	99%
Intermediate Calculations
Sample Size	5
Degrees of Freedom	3
t Value	5.840909
XBar, Sample Mean of X	5.8
Sum of Squared Differences from XBar	18.8
Standard Error of the Estimate	3.769512
h Statistic	0.202128
Predicted Y (YHat)	5.819149
For Average Y
Interval Half Width	9.8987
Confidence Interval Lower Limit	-4.0796
Confidence Interval Upper Limit	15.71786
For Individual Response Y
Interval Half Width	24.1402
Prediction Interval Lower Limit	-18.3211
Prediction Interval Upper Limit	29.95935

a )the 0.99 confidence interval for the mean predicted when x = 6 is (-4.0796 ,15.71786)

b ) the 0.99 prediction interval for an individual predicted when x = 6. is (-18.3211 ,29.95935)