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) 1282 1296 1332 1336 1354 1390 1401 1425 1439 1447
Find the equation of the line of best fit. Round to two decimal places as needed. Choose the correct answer below.
A. y = 19.28x - 37,247.71 B. y = 19.28x + 37,247.71
C. y = -37,247. 71 + 19.28 D. y = -37,247.71
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 using a graphing calculator, follow these steps:
1. Enter the x-values (years) in L1 and the y-values (tickets sold) in L2 in the lists on the calculator.
2. Press the STAT button.
3. Press the right-arrow key to access the CALC menu.
4. Choose option 4: LinReg(ax+b).
5. Press ENTER.
6. The calculator will display the equation of the line of best fit in the form of y = ax + b. Round the coefficients a and b to two decimal places as needed.
The equation of the line of best fit for the given data is y = 19.28x - 37,247.71.
To find the correlation coefficient, follow these steps:
1. Press the STAT button.
2. Press the right-arrow key to access the CALC menu.
3. Choose option 8: LinReg(a+bx).
4. Press ENTER.
5. The calculator will display the correlation coefficient r. Round it to three decimal places as needed.
The correlation coefficient for the given data is 0.915.
To predict the number of movie tickets sold in 2014, substitute x = 2014 into the equation of the line of best fit and solve for y:
y = 19.28(2014) - 37,247.71
y ≈ 38,992.72
Therefore, the predicted number of movie tickets sold in 2014 is approximately 38,992.72.