Question

Question 1

a) For the data in Homework 2, Question 1, calculate the ANOVA table. Use the ANOVA Table to conduct an F-Test to see if the model is significant (use α = 0.05).

Data:

Size (Xi)	12	15	18	21	24	27
Price (Yi)	60	85	75	105	120	110

b) Give a 95% confidence interval for the mean sale price for 2000 sq. ft. houses.

c)   Give a 95% prediction interval for the sale price of an individual 2000 sq. ft. house.

d)   For the data in Homework 2, Question 2, calculate the ANOVA table for the data. Use the ANOVA Table to conduct an F-Test to see if the model is significant (use α = 0.05).

Data:

dollars	satisfaction
11	6
18	8
17	10
15	4
9	9
5	6
12	3
19	5
22	2
25	10

Question 2

A research firm collected data on a sample of n = 30 drivers to investigate the relationship between the age of a driver and the distance the driver can see. The data is given below:

Age	Distance		Age	Distance
18	510		55	420
20	590		63	350
22	560		65	420
23	510		66	300
23	460		67	410
25	490		68	300
27	560		70	390
28	510		71	320
29	460		72	370
32	410		73	280
37	420		74	420
41	460		75	460
46	450		77	360
49	380		79	310
53	460		82	360

Use SAS to fit a simple linear regression and answer the following questions:

a) Find the least squares estimate for the regression line Y_i = b₀ + b₁X_i + e_i.

b) Estimate the standard deviation of the error term e_i

c)   Test the null hypothesis that b₁ = 0, using α = 0.05. Is the model useful?

d)   Calculate R²? Explain what this means, and comment on whether or not it suggests the model is good.

e)   Calculate the correlation coefficient? Explain what this means, and comment on whether or not it suggests the model is good.

f)    What would you expect the distance that a 50 year old driver can see to be?

g)   Give a 95% prediction interval for the distance that an individual 50 year old can see.

h) Give a 95% confidence interval for the mean distance that 50 year olds can see.

Answer 1

a) Enter the data in excel -> Data -> data analysis -> Regression -> Ok -> in Input Y range select the cells containing the y values -> In Input X range select the cells containing the x values -> In output range select any empty cell -> Ok -> The output appears as:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.896015
R Square	0.802844
Adjusted R Square	0.753555
Standard Error	11.40175
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	1	2117.5	2117.5	16.28846	0.015657
Residual	4	520	130
Total	5	2637.5
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	21	18.31731	1.146457	0.315525	-29.857	71.857	-29.857	71.857
X Variable 1	3.666667	0.908514	4.035897	0.015657	1.144229	6.189105	1.144229	6.189105

The Anova table in the output.

b)

d) Enter the data in excel -> Data -> data analysis -> Regression -> Ok -> in Input Y range select the cells containing the satisfaction -> In Input X range select the cells containing dollars -> In output range select any empty cell -> Ok -> The output appears as:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.076446
R Square	0.005844
Adjusted R Square	-0.11843
Standard Error	6.481938
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1.975843	1.975843	0.047027	0.833749
Residual	8	336.1242	42.01552
Total	9	338.1
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	14.27126	5.167806	2.761569	0.024615	2.354273	26.18824	2.354273	26.18824
X Variable 1	0.163293	0.753001	0.216856	0.833749	-1.57313	1.899717	-1.57313	1.899717

The Anova table appears in the output.