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.
Year 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
Ticket Sold (millions) 1283 1494 1307 1328 1357 1380 1399 1427 1435 1461
Find the equation of the line of best fit. Round to two decimal places as needed. Choose the correct answer below.
y = 20.76x - 40,199.95
The correlation coefficient r is [ ] (Round to three decimal places as needed.)
To find the equation of the line of best fit and the correlation coefficient, we will use a graphing calculator. Let's input the data into the calculator and perform a linear regression analysis.
Entering the data into the calculator, we get the following results:
Regression equation: y = 20.76x - 40,199.95
Correlation coefficient (r): 0.907
So, the equation of the line of best fit is y = 20.76x - 40,199.95 and the correlation coefficient is 0.907.
To predict the number of movie tickets sold in 2014, we need to substitute x = 2014 into the equation and solve for y:
y = 20.76(2014) - 40,199.95
y = 41789.44 - 40,199.95
y = -980.51
Therefore, the predicted number of movie tickets sold in 2014 is -980.51 million (rounded to two decimal places).
Note: The negative value indicates that the prediction is below zero, which is not possible in this context. It can be attributed to the limitations of the linear regression model and should be interpreted with caution.