Exercise 3 Page 205

The attendance y (in thousands) at the amusement park from 2005 to 2014 is given as follows.

Year,	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014
x	0	1	2	3	4	5	6	7	8	9
Attendance, y	850	845	828	798	800	792	785	781	775	760

To find a line of fit for the data we will use the linear regression analysis tool in our calculator.

Finding Line of Fit

First we enter the data points in the calculator. Ppress the STAT button, and then select the option Edit. We then enter the data points' x-values in list L_1, and the corresponding y-values in L_2.

The window in the calculator, which shows Stat and then Edit

Calculator that shows two lists where values have been entered

After we have entered the values, we press the STAT button. Then we select CALC and the option LinReg(ax+b). The calculator then makes a linear regression of the data.

Counter that displays the list of CALC and where you have chosen LinReg

Illustration of the LinReg(ax+b) window on the calculator

That gives us the following line of best fit for the data. y=-9.58788x+844.545

Approximating Attendance in 2017

We are asked to use this model to extrapolate what the approximate attendance levels will be in the year 2017. Recall that that x=0 corresponds to the year 2005. Let's find the value of x that corresponds to 2017. 2017-2005= 12 Now we can substitute 12 for x into the equation of the line of best fit.

y=-9.58788x+844.545

Substitute

x= 12

y=-9.58788( 12)+844.545

Multiply

y=-115.05456+844.545

AddTerms

Add terms

y=729.49044

We are also told that the y values are measured in thousands. Therefore, to express the predicted attendance, we need to multiply our answer by 1000.

729.49044

Mult