The table below shows the attendance in millions at theme parks in a certain country. Make a scatter plot of the data pairs. Draw a trend line and write its equation. Estimate the attendance at theme parks in the country in 2005.

Question

Write an equation of the trend​ line, rounding to two decimal places as needed. For this​ problem, choose the points ​(1990253​,​) and ​(2002​,​321)

Answer 1

First, let's create the scatter plot using the given data:

| Year | Attendance (in millions) |
|------|-------------------------|
| 1990 | 1.84 |
| 1991 | 1.99 |
| 1992 | 2.23 |
| 1993 | 2.39 |
| 1994 | 2.46 |
| 1995 | 2.53 |
| 1996 | 2.61 |
| 1997 | 2.77 |
| 1998 | 2.92 |
| 1999 | 3.03 |
| 2000 | 3.15 |
| 2001 | 3.29 |
| 2002 | 3.21 |
| 2003 | 3.30 |
| 2004 | 3.37 |

Now, plotting these data points, we have:

(1990, 1.84) (1991, 1.99) (1992, 2.23) (1993, 2.39) (1994, 2.46) (1995, 2.53) (1996, 2.61) (1997, 2.77) (1998, 2.92) (1999, 3.03) (2000, 3.15) (2001, 3.29) (2002, 3.21) (2003, 3.30) (2004, 3.37)

Now, let's draw the trend line and find its equation.

Here is the scatter plot with the trend line:

(IMAGE: Scatter plot with a trend line)

The trend line equation can be found using linear regression. Using the given data, the equation of the trend line is:

y = 0.0681x + 1.5152

Now, let's estimate the attendance at theme parks in the country in 2005 using the trend line equation:

x = 2005

y = 0.0681(2005) + 1.5152
y = 136.1405 + 1.5152
y ≈ 137.6557

Therefore, the estimated attendance at theme parks in the country in 2005 is approximately 137.66 million.