The U.S. Census Bureau publishes information on the population of the United States in Current Population Reports.

vazelinahS 2021-01-07 Answered

The U.S. Census Bureau publishes information on the population of the United States in Current Population Reports. The following table gives the resident U.S. population, in millions of persons, for the years 1990-2009. Forecast the U.S. population in the years 2010 and 2011

YearPopulation (millions)19902501991253199225719932601994263199526619962691997273199827619992792000282200128520022882003290200429320052962006299200730220083042009307

a) Obtain a scatterplot for the data.

b) Find and interpret the regression equation.

c) Mace the specified forecasts.

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Expert Answer

Jaylen Fountain
Answered 2021-01-08 Author has 170 answers

a) Year is on the horizontal axis and population is on the vertical axis. image b) Let us first determine the necessary sums:  xi=3990
 xi2=79960670
 yi=5592
 xi yi=11183199 Next, we can determine Sxx and Sxy
Sxx=  xi2  ( xi)2n=79960670  3990220=665
Sxy=  xiyi  ( xi)( yi)n=11183199  3990  559220=1995 The estimate b of the slope β is the ratio of Sxy and Sxx: b= SxySxx= 1995665=3 The mean is the sum of all values divided by the number of values: x=  xin= 699020=1999.5
y=  yin= 559220=279.6 The estimate a of the intercept α is the average of u decreased by the product of the estimate of the slope and the average of x. a= y  bx=279.6  3  1999.5= 5718.9 General least-squares equation: y^= α + β x. Replace α by a= 5505.3432 and β by b=2.8930 in the general least-squares equation: y=a + bx= 5718.9 + 3x

c) Let us evaluate the regression line of part (b) at x=2010 and x=2011. y= 5718.9 + 3(2010)=311.1
y= 5718.9 + 3(2011)=314.1 Thus the predicted U.S. population in 2010 is 311.1 million and predicted U.S. population in 2011 is 314.1 million.

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