Each student in a sample of lo was asked for the distance an

Each student in a sample of lo was asked for the distance and the time required to commute to college yesterday. The data collected are shown in the table. Distance 1 1 2 5 6 6 7 9 11 12 Time 5 10 5 15 10 15 15 15 25 25 Given an equation for the line of best fit of y = 4.22 + 1.63x, se^2 = 9.1440, sigma x = 60, and SS(x) = 138, make the following estimates. (a) Give a point estimate for the mean time required to commute 4 miles. (Give your answer correct to two decimal places.) (b) Give a 9O% confidence inter-val for the mean travel time required to commute 4 miles. (Give your answers correct to two decimal places.) (c) Give a 90% prediction interval for the travel time required for one person to commute the 4 miles. (Give your answers correct to two decimal places.) lower limit upper limit

Solution

(b)

Lower limit = 8.72

Upper limit = 12.76

(c)

Lower limit = 4.76

Upper limit = 16.71

I have attached the corresponding excel sheet on the link given below.

https://drive.google.com/file/d/0ByUkX0Zrq3LBR0J3LUtsTUFLZTQ/view?usp=sharing

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.913
R Square	0.834
Adj. R Square	0.813
Standard Error	3.024
Observations	10.000
ANOVA
	df	SS	MS	F	Significance F
Regression	1.000	366.848	366.848	40.119	0.000
Residual	8.000	73.152	9.144
Total	9.000	440.000
	Coefficients	Standard Error	t Stat	P-value	Lower 90.0%	Upper 90.0%
Intercept	4.217	1.817	2.322	0.049	0.839	7.595
Distance	1.630	0.257	6.334	0.000	1.152	2.109
The regression equation is Time-hat=4.217+1.630*Distance		Mean =	6.00
					St. Dev. =	3.92
Desired Pred. Level	90%	alpha	10%
Prediction at	Point	critical	St. Error	Margin of	Lower	Upper	Interval
Distance	Prediction	t-value	of Prediction	Error	Bound	Bound	Length
4	10.74	1.86	3.21	5.97	4.76	16.71	11.95
Desired Conf. Level	90%	alpha	10%
Confidence at	Point	critical	Standard	Margin of	Lower	Upper	Interval
Distance	Prediction	t-value	Error	Error	Bound	Bound	Length
4	10.74	1.86	1.09	2.02	8.72	12.76	4.04