Deriving the regression equation, testing the model fit and obtain confidence interval for a given values.
The data below contains the population of the United States for the years 1930 through 1999. Fit a linear trend to these data.
a) What is the resulting regression equation?
b) What percentage of the variation in y has been explained by the regression?
c) Based on your answer in part b and on any other regression results you obtain, how well does the equation fit the data? Does a good fit ensure that forecasts for future years would be accurate?
d) Use the equation developed to predict the U.S. population in the years 2000 and 2001. Find out a point prediction and a 95 percent prediction interval.
e) How reliable do you believe the forecast in part d might be? What factors might influence this correctness?
|
YEAR
|
POPULATION
|
|
1930
|
123,076,741
|
|
1931
|
124,039,648
|
|
1932
|
124,840,471
|
|
1933
|
125,578,763
|
|
1934
|
126,373,773
|
|
1935
|
127,250,232
|
|
1936
|
128,053,180
|
|
1937
|
128,824,829
|
|
1938
|
129,824,939
|
|
1939
|
130,879,718
|
|
1940
|
132,122,446
|
|
1941
|
133,402,471
|
|
1942
|
134,859,553
|
|
1943
|
136,739,353
|
|
1944
|
138,397,345
|
|
1945
|
139,928,165
|
|
1946
|
141,388,566
|
|
1947
|
144,126,071
|
|
1948
|
146,631,302
|
|
1949
|
149,188,130
|
|
1950
|
152,271,417
|
|
1951
|
154,877,889
|
|
1952
|
157,552,740
|
|
1953
|
160,184,192
|
|
1954
|
163,025,854
|
|
1955
|
165,931,202
|
|
1956
|
168,903,031
|
|
1957
|
171,984,130
|
|
1958
|
174,881,904
|
|
1959
|
177,829,628
|
|
1960
|
180,671,158
|
|
1961
|
183,691,481
|
|
1962
|
186,537,737
|
|
1963
|
189,241,798
|
|
1964
|
191,888,791
|
|
1965
|
194,302,963
|
|
1966
|
196,560,338
|
|
1967
|
198,712,056
|
|
1968
|
200,706,052
|
|
1969
|
202,676,946
|
|
1970
|
205,052,174
|
|
1971
|
207,660,677
|
|
1972
|
209,896,021
|
|
1973
|
211,908,788
|
|
1974
|
213,853,928
|
|
1975
|
215,973,199
|
|
1976
|
218,035,164
|
|
1977
|
220,239,425
|
|
1978
|
222,584,545
|
|
1979
|
225,055,487
|
|
1980
|
227,224,681
|
|
1981
|
229,465,714
|
|
1982
|
231,664,458
|
|
1983
|
233,791,994
|
|
1984
|
235,824,902
|
|
1985
|
237,923,795
|
|
1986
|
240,132,887
|
|
1987
|
242,288,918
|
|
1988
|
244,498,982
|
|
1989
|
246,819,230
|
|
1990
|
249,464,396
|
|
1991
|
252,153,092
|
|
1992
|
255,029,699
|
|
1993
|
257,782,608
|
|
1994
|
260,327,021
|
|
1995
|
262,803,276
|
|
1996
|
265,228,572
|
|
1997
|
267,783,607
|
|
1998
|
270,248,003
|
|
1999
|
272,690,813
|