Scientists have predicted that an increase in sea level is one of the likely consequences of climate change associated with the enhanced greenhouse effect. The sea level of a particular place is...

Scientists have predicted that an increase in sea level is one of the likely consequences of
climate change associated with the enhanced greenhouse effect. The sea level of a particular
place is measured using tide gauges. A tide gauge is a device built to measure water-level
variations due to tides and weather and to eliminate effects due to waves. The file
Assignment2-Q2.xls contains time series data on sea level at Fort Denison in Sydney Harbour
from 1949 to 2006. Consider the simple regression model

SEALEVEL =
_0

+_1
YEAR +
_
(a) Estimate this model and report the results.
(b) Interpret the estimate for _1.
(c) Why is it difficult to interpret the estimate for _0?
(d) Test a null hypothesis that the average sea level is not changing against an alternative
that it is changing over time. Use a 5% significance level.
(e) Without carrying out a formal hypothesis test, can you say immediately what the test
decision in (d) would be if the alternative was that the average sea level is increasing?
(f) Predict the sea level in 2008.
(g) Find a 95% interval prediction for the sea level in 2008 (Hint: you may use Excel
command =DEVSQ(A#:A##) to calculate
SS
x.)

SOURCE	http://www.pol.ac.uk/psmsl/pubi/met.monthly.data/680140.metdata
mean sea level for each year at fort denison in sydney harbour (mm's)
Year	mm's
1949	912
1950	938
1951	951
1952	933
1953	914
1954	913
1955	960
1956	977
1957	925
1958	947
1959	920
1960	927
1961	897
1962	932
1963	922
1964	977
1965	924
1966	928
1967	919
1968	951
1969	906
1970	923
1971	943
1972	921
1973	959
1974	988
1975	958
1976	991
1977	942
1978	973
1979	919
1980	948
1981	962
1982	912
1983	908
1984	964
1985	958
1986	957
1987	926
1988	970
1989	977
1990	995
1991	964
1992	956
1993	920
1994	930
1995	936
1996	948
1997	901
1998	966
1999	955
2000	977
2001	1019
2002	963
2003	958
2004	954
2005	968
2006	950

Question 3
A developer who specializes in summer cottage property is considering purchasing a large
tract of land adjoining a lake. The current owner of the tract has already subdivided the
land into separate building lots and has prepared the lots by removing some of the trees. The
Developer wants to forecast the value of each lot. From previous experience, she knows
that the most important factors affecting the price of the lot are size (lot size), number of
mature trees (Trees), and distance to the lake (Distance). From a nearby area, she gathers
data for 60 recently sold lots. These data are stored in Assignment2-Q3.xls.
(a) Perform a multiple regression in Excel and provide excel output for the regression
model_____ _ __ _____ _____ _________ ____________ _
(b) Write down the equation for regression line.
(c) What is the standard error of estimate? Interpret its value.
(d) What is the coefficient of determination? What does this statistic tell you?
(e) What is the coefficient of determination, adjusted for degrees of freedom? Why does
this value differ from the coefficient of determination? What does this tell you about
the model?
(f) Test the overall utility of the model. What does the p-value of the test statistic tell
you?
(g) Interpret each of the coefficients.
(h) Test to determine whether each of the independent variables is linearly related to the
price of the lot

Price (Thousands of $)	Lot-size (Hundreds of m2)	number of mature Trees	Distance to the lake in meters
105.4	41.2	24	42
91.2	44.8	5	71
183.3	21.3	72	43
93.8	43.9	58	14
207.5	57.7	52	12
130.9	33.4	78	26
162.3	31.4	65	51
18.8	27.4	22	0
80.5	26.2	68	83
38.3	40.0	57	76
71.3	47.6	53	35
55.5	31.6	36	26
85.7	21.6	23	24
110.5	36.3	48	98
85.1	47.2	61	59
78.3	30.5	41	55
27.2	41.8	1	60
70.9	20.6	20	33
101.4	35.3	38	75
133.3	40.1	68	0
117.7	35.6	24	41
49.7	20.6	16	77
49.6	22.4	32	86
83.2	45.8	77	19
81.3	29.4	40	0
152.5	51.7	60	34
112.2	27.2	0	16
37.1	37.0	50	49
130.2	38.9	48	63
39.1	32.5	25	45
81.9	34.0	12	0
24.6	35.8	16	34
101.9	32.9	44	42
117.6	46.4	62	48
148.8	51.9	59	39
60.2	28.9	0	66
43.7	35.2	57	77
113.1	30.4	70	78
38.1	38.3	24	62
89.2	49.2	61	0
3.0	21.5	46	83
55.8	41.9	10	69
89.7	21.8	79	62
136.1	66.3	56	34
44.7	28.2	73	77
63.2	41.9	64	65
163.4	46.7	69	27
64.1	32.1	12	0
98.7	38.5	59	77
139.9	27.6	0	0
92.0	47.0	65	37
66.6	20.7	24	51
16.4	34.0	12	75
131.9	31.9	76	63
11.0	28.0	2	42
27.9	40.0	52	84
103.5	46.6	26	70
107.0	23.2	11	83
51.6	46.4	53	44
133.4	32.1	55	98