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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 describeed 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

 

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