Question

Use this linear model to predict the U.S. population in $1890$. Show your work.

Short answer

The regression line,$\hat{y}=53.10281$.

Step-by-step solution

Given Information

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 $1790$to$1880$.

Explanation

The general equation will be as:

$\hat{y}=a+bx$

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

$a=-1.19311$

$b=0.0287280$

Thus, the regression line is as:

$\hat{y}=a+bx$

$\Rightarrow \hat{y}=-1.19311+0.0287280x$

Thus, evaluating the regression line we will get that,

$\hat{y}=a+bx$

$\Rightarrow \hat{y}=-1.19311+0.0287280x$$\Rightarrow \hat{y}=-1.19311+0.0287280\times 1890$

$\Rightarrow \hat{y}=53.10281$