Question 460930
a)find a linear model using the years 0 and 4
<pre>
Find the equation of a line through the points

(0,11.807) and (4,29.349)

m = {{{(y[2]-y[1])/(x[2]-x[1])=(29.349-11.807)/(4-0) = 4.3855}}}

then use 

y - y<sub>1</sub> = m(x - x<sub>1</sub>)

y - 11.807 = 4.3855(x - 0)

y - 11.807 = 4.3855x

         y = 4.3855x + 11.807

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</pre>
b)find a linear model using the graphing calculator.
<pre>
press CLEAR
press STAT
press the right arrow key to highlight CALC
press 4
You will see 

               LinReg(ax+b)

Press ENTER
You will see
               LinReg 
                y=ax+b
                a=5.6524
                b=8.731
                rē=.9861609225
                r=.9930563541

The equation of the line is y = 5.6524x + 8.731

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</pre>
c)what is the correlation coefficient?
<pre>
That's the value of r, which is r=.9930563541

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</pre>
d)use your model to predict the numbers for 2010.
<pre>
1995, 0 
1997, 2
1999, 4
2001, 6 
2003, 8 
2005, 10 

Extend this list by 2's:

2007, 12
2009, 14
2011, 16

Since 2010 is halfway between 2009, 14 and 2011 16,
we must have 2010 as 15.

So we substitute 15 for x in the formula:

y = 5.6524x + 8.731
y = 5.6524(15) + 8.731
y = 93.517

Edwin</pre>