Chapter 4.6, Problem 8PPS

To determine

If $\left(x\right)$ be the number of years since 2000 then find the equation of regression line for the data shown below.

Year	2002	2003	2004	2005	2006	2007
Sites Rented	34	45	42	53	58	47

Answer to Problem 8PPS

The equation for regression line is $y=3.066x+32.71$ .

Explanation of Solution

Given:

The given data is shown as,

Year	2002	2003	2004	2005	2006	2007
Sites Rented	34	45	42	53	58	47

Calculation: Plugging $\left(x=0\right)$ for the year 2000 in the calculator and obtaining equation for the regression line using the calculator for the given data is written as,

  $y=3.066x+\mathrm{32.71......}\left(1\right)$

To determine

The predicted number of campsites that will be rented in 2010.

Answer to Problem 8PPS

The predicted number of campsites that will be rented in 2010 are 64.

Explanation of Solution

Given:

The given data is shown as,

Year	2002	2003	2004	2005	2006	2007
Sites Rented	34	45	42	53	58	47

Calculation: Plugging $\left(x=2010-2000\right)$ for the year 2010 in the (1) and simplifying.

  $\begin{array}{c}y=3.066\left(10\right)+\mathrm{32.71......}\left(\text{Plugging }x=10\right)\\ =63.37\end{array}$

Hence, the number of campsites that will be rented in 2010 will 64 approx.

To determine

The predicted number of campsites that will be rented in 2020.

Answer to Problem 8PPS

The predicted number of campsites that will be rented in 2020 are 94.

Explanation of Solution

Given:

The given data is shown as,

Year	2002	2003	2004	2005	2006	2007
Sites Rented	34	45	42	53	58	47

Calculation: Plugging $\left(x=2020-2000\right)$ for the year 2020 in the (1) and simplifying.

  $\begin{array}{c}y=3.066\left(20\right)+\mathrm{32.71......}\left(\text{Plugging }x=20\right)\\ =94.03\end{array}$

Hence, the number of campsites that will be rented in 2020 are94.