Question

Given are five observations for two variables, x and y.

x i	1	2	3	4	5
y i	4	8	6	11	14

Round your answers to two decimal places.

a. Using the following equation:

Estimate the standard deviation of ŷ* when x = 3.

b. Using the following expression:

Develop a 95% confidence interval for the expected value of y when x = 3.

  to  

c. Using the following equation:

Estimate the standard deviation of an individual value of y when x = 3.

d. Using the following expression:

Develop a 95% prediction interval for y when x = 3. If your answer is negative, enter minus (-) sign.

  to  

Answer 1

using excel>Addin>phstat>Regression

we have

Simple Linear Regression Analysis
Regression Statistics
Multiple R	0.9149
R Square	0.8370
Adjusted R Square	0.7827
Standard Error	1.8529
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	52.9000	52.9000	15.4078	0.0294
Residual	3	10.3000	3.4333
Total	4	63.2000
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	1.7000	1.9434	0.8748	0.4461	-4.4847	7.8847
x	2.3000	0.5859	3.9253	0.0294	0.4353	4.1647

Confidence Interval Estimate
Data
X Value	3
Confidence Level	95%
Intermediate Calculations
Sample Size	5
Degrees of Freedom	3
t Value	3.182446
XBar, Sample Mean of X	3
Sum of Squared Differences from XBar	10
Standard Error of the Estimate	1.852926
h Statistic	0.2
Predicted Y (YHat)	8.6
For Average Y
Interval Half Width	2.6371
Confidence Interval Lower Limit	5.9629
Confidence Interval Upper Limit	11.23715
For Individual Response Y
Interval Half Width	6.4597
Prediction Interval Lower Limit	2.1403
Prediction Interval Upper Limit	15.05966

a. the standard deviation of ŷ* when x = 3. is 1.853

b.)a 95% confidence interval for the expected value of y when x = 3.

5.963 to  11.237

c. the standard deviation of an individual value of y when x = 3. is 2.030

d. a 95% prediction interval for y when x = 3.

2.140 to 15.060