Question

use a graphing calculator to find the equation of the line of best fit for the data in the table below. find the value of the correlation coefficient r. then predict the number of movie tickets sold in 2014. let x represent the number of years after 1990.

year	1998	1999	2000	2001	2002	2003	2004	2005	2006	2007
tickets sold (millions)	1282	1305	1327	1332	1357	1377	1402	1419	1444	1452

a. y = 1.12781x + 19.35
b. y = 19.35x + 1127.81
c. y = 1.12781
d. y = 19.35x - 1127.81
the correlation coefficient r is (round to three decimal places as needed.)

Explanation:

Step1: Enter data into calculator

Enter years (x - values: 8, 9, 10, 11, 12, 13, 14, 15, 16, 17) and tickets - sold (y - values: 1282, 1305, 1327, 1332, 1357, 1377, 1402, 1419, 1444, 1452) into a graphing calculator.

Step2: Find line - of - best - fit

Use the linear regression function on the graphing calculator. The general form of a linear regression equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. For this data, the line of best fit is $y=19.35x + 1127.81$, so the correct equation choice is B.

Step3: Find correlation coefficient

Use the graphing calculator's function to find the correlation coefficient $r$. After calculation, $r\approx0.997$ (rounded to three decimal places).

Step4: Predict for 2014

For 2014, $x = 2014 - 1990=24$. Substitute $x = 24$ into the equation $y=19.35x + 1127.81$.
$y=19.35\times24 + 1127.81$
$y = 464.4+1127.81$
$y = 1592.21$

Answer:

Equation: B. $y = 19.35x+1127.81$
Correlation coefficient: $0.997$
Prediction for 2014: $1592.21$ million tickets