Chapter 12.2, Problem 1.3CYU

To determine

To use this linear model to predict the U.S. population in $1890$ .

Answer to Problem 1.3CYU

  $\widehat{y}=53.10281$ .

Explanation of Solution

Now, it is given in the question that variable x be the number of the years since $1700$ and the variable y be the U.S. population in the years $\text{1790 to 1880}$ . Thus, the general equation will be as:

  $\widehat{y}=a+bx$

And the slope and the constant of the regression line is give in the previous question as:

  $\begin{array}{l}a=-1.19311\\ b=0.0287280\end{array}$

Thus, the regression line is as:

  $\begin{array}{l}\widehat{y}=a+bx\\ \Rightarrow \widehat{y}=-1.19311+0.0287280x\end{array}$

Thus, evaluating the regression line we will get that,

  $\begin{array}{l}\widehat{y}=a+bx\\ \Rightarrow \widehat{y}=-1.19311+0.0287280x\\ \Rightarrow \widehat{y}=-1.19311+0.0287280\times 1890\\ \Rightarrow \widehat{y}=53.10281\end{array}$