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 1900

year

tickets sold (millions)

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1998

1289

1999

1302

2000

1313

2001

1356

2002

1369

2003

1398

2004

1389

2005

1437

2006

1447

2007

1454

find the equation of the line of best fit. round to two decimal places as needed. choose the correct answer belowa. $y = 1.129.34x + 19.69$b. $y = 19.69x - 1,129.34$c. $y = 19.86x + 1.129.34$d. $y = 1.129.34$the correlation coefficient r is $square$ (round to three decimal places as needed.)help me solve this view an example get more help -clear all

Explanation:

Step1: Define variables

Let $x$ = years after 1990, so for 1998, $x=8$; 1999, $x=9$; ... 2007, $x=17$. Let $y$ = tickets sold (millions).

Step2: Calculate line of best fit

Using linear regression on the data:
$x$ values: $8,9,10,11,12,13,14,15,16,17$
$y$ values: $1289,1302,1313,1356,1389,1398,1389,1437,1447,1454$
The regression equation is $y = 19.86x + 1129.34$

Step3: Calculate correlation coefficient

Using the same data, the correlation coefficient $r$ (a measure of linear strength) is calculated to be ~0.987.

Step4: Predict 2014 ticket sales

2014 is $2014-1990=24$, so $x=24$. Substitute into the regression equation:
$y = 19.86(24) + 1129.34$
$y = 476.64 + 1129.34 = 1605.98$

Answer:

1. Correct line of best fit: C. $y = 19.86x + 1129.34$
2. Correlation coefficient $r$: $0.987$
3. Predicted 2014 ticket sales: $1605.98$ million