Chapter 1, Problem 53SGA

a.

To determine

To graph: the given data on scatter plot.

Answer to Problem 53SGA

  

Explanation of Solution

Given information:

Year	1994	1995	1996	1997	1998	1999	2000	2008
Visitors	18458	20639	22658	24194	23698	24466	25975	?

Calculation:

Let the year be x and the number of visitors be y. Plot of the graph from the given data will be as follows:

  

b.

To determine

To find: the equation of a best fit line by using two ordered pairs.

Answer to Problem 53SGA

  $y=1310x-2593682$

Explanation of Solution

Given information:

Year	1994	1995	1996	1997	1998	1999	2000	2008
Visitors	18458	20639	22658	24194	23698	24466	25975	?

Calculation:

Select any two ordered pairs like $\left(1994,18458\right)$ and $\left(1998,23698\right)$ , and substitute the values in the slope formula as shown below.

  $\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{23698-18458}{1998-1994}\\ =\frac{5240}{4}\\ =1310\end{array}$

Put any point coordinate and slope value into the slope intercept formula and evaluate the y -intercept as follows:

  $\begin{array}{c}y=mx+b\\ 18458=1310\left(1994\right)+b\\ 18458=2612140+b\\ b=18458-2612140\\ =-2593682\end{array}$

Now, put the values of slope and b into the slope intercept formula as follows:

  $\begin{array}{l}y=mx+b\\ y=1310x-2593682\end{array}$

Thus, the equation is $y=1310x-2593682$ .

c.

To determine

To find: the equation of regression line and its correlation value by using a graphing calculator.

Answer to Problem 53SGA

  $y=1115.8928571429x-2205568.3214286$

  $r=0.94412757444791$

Explanation of Solution

Given information:

Year	1994	1995	1996	1997	1998	1999	2000	2008
Visitors	18458	20639	22658	24194	23698	24466	25975	?

Calculation:

From the graph

  

By using the graphing calculator, we get slope value as 1115.8928571429 and intercept value as $-2205568.3214286$ .

Now, put the values in the following equation and evaluate regression of equation of line

  $\begin{array}{l}y=mx+b\\ y=1115.8928571429x-2205568.3214286\end{array}$

Thus, the regression line equation is, $y=1115.8928571429x-2205568.3214286$ .

By using graphing calculator, the value of correlation coefficient ( r ) is $0.94412757444791$ .

d.

To determine

To explain: the whether the relationship predicted by the equation for the number of visitors in 2008 is reliable.

Answer to Problem 53SGA

35 million

Explanation of Solution

Given information:

Year	1994	1995	1996	1997	1998	1999	2000	2008
Visitors	18458	20639	22658	24194	23698	24466	25975	?

  $y=1115.8928571429x-2205568.3214286$

  $r=0.94412757444791$

Calculation:

Since $0.75\le r\le 1$ , the equation of the regression line shows a strong relationship.

Putting the value of $x=2008$ , into the equation, we get

  $\begin{array}{c}y=1115.8928571429\left(2008\right)-2205568.3214286\\ y=35144.535714343656\end{array}$

This suggests that each year more and more people visit the U.S from overseas. The reason behind the steadily increasing number of visitors is not known. It may be due to increase in population, more people travel, or maybe travel to U.S is easier.

35 million visitors seem like a reasonable number. It doesn't exceed the world population.