Chapter 2, Problem 1CE

To determine

To prove: The least square regression line that models these data (with rounded coefficients) is $y=-146.1x+2330$.

Explanation of Solution

Given:

Year	Housing Units
2002	1648
2003	1679
2004	1842
2005	1931
2006	1979
2007	1503
2008	1120
2009	794
2010	652
2011	585
2012	650

$x=2$ corresponds to the year $2002$.

Formula used:

The least square regression line that models any data is given by

$y=ax+b$

Proof:

All the year are data for $x$ and all the housing units are data for $y$.

Step 1. In the $\text{TI-83}$ calculator, press the $\text{STAT, 5, ENTER}$ button.

Step 2. Then press the $\text{STAT, ENTER}$ button.

Step 3. If there is data in any of the editor, clear it using $\text{CLEAR, ENTER}$ buttons.

Step 4. Enter the $x$ data in $L1$ and $y$ data in $L2$ by using arrow buttons, typing the data and pressing the $\text{ENTER}$.

Step 5. When done press $\text{STAT}$, right arrow to select $\text{CALC, 4 and ENTER}$ to confirm.

So, the linear model will be:

$\begin{array}{ccc}\hfill y& =& ax+b\hfill \\ \hfill a& =& -146.1\hfill \\ \hfill b& =& 2330.336364\hfill \\ \hfill r^2& =& .7570183599\hfill \end{array}$

Solve ahead as,

$r=.8700680203$

Therefore,

The value of $a=-146.1\text{ and }b\approx 2330$

So, $y=-146.1x+2330$