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

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

$\begin{array}{|cc|}\hline \text{Year}& \text{Population (millions)}\\ 1990& 250\\ 1991& 253\\ 1992& 257\\ 1993& 260\\ 1994& 263\\ 1995& 266\\ 1996& 269\\ 1997& 273\\ 1998& 276\\ 1999& 279\\ 2000& 282\\ 2001& 285\\ 2002& 288\\ 2003& 290\\ 2004& 293\\ 2005& 296\\ 2006& 299\\ 2007& 302\\ 2008& 304\\ 2009& 307\\ \hline\end{array}$

a) Obtain a scatterplot for the data.

b) Find and interpret the regression equation.

c) Mace the specified forecasts.

You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Jaylen Fountain

a) Year is on the horizontal axis and population is on the vertical axis. b) Let us first determine the necessary sums:

Next, we can determine ${S}_{xx}$ and ${S}_{xy}$

The estimate b of the slope $\beta$ is the ratio of ${S}_{xy}$ and ${S}_{xx}$: The mean is the sum of all values divided by the number of values:
The estimate a of the intercept $\alpha$ is the average of u decreased by the product of the estimate of the slope and the average of x. General least-squares equation: . Replace $\alpha$ by and $\beta$ by $b=2.8930$ in the general least-squares equation:

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