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) 1281 1304 1305 1348 1363 1378 1408 1417 1448 1460
Find the equation of the line of best fit. Round to two decimal places as needed. Choose the correct answer below.
A. y = -39,576.89x + 20.45 B. y = 20.45x - 39,576.89
C. y = -39,576.89 D. y = 20.45x + 39,576.89
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 can use a graphing calculator. Here are the steps:
1. Enter the data into the calculator.
2. Plot the points on a scatterplot.
3. Use the calculator to find the equation of the line of best fit.
4. Read the equation and correlation coefficient from the calculator.
After performing these steps, the equation of the line of best fit should be:
y = 20.45x - 39,576.89
The correct answer is B.
To find the correlation coefficient, we need to check the output or settings on the calculator. However, without this information, we cannot provide the value of the correlation coefficient.
The predicted number of movie tickets sold in 2014 is [ ].
(Round to the nearest whole number as needed.)
To predict the number of movie tickets sold in 2014 using the equation of the line of best fit, we substitute 2014 for x in the equation.
y = 20.45x - 39,576.89
y = 20.45 * 2014 - 39,576.89
y ≈ 41,243.3
Rounding to the nearest whole number, the predicted number of movie tickets sold in 2014 is 41,243.
To find the equation of the line of best fit and the correlation coefficient using a graphing calculator, follow these steps:
1. Enter the data points into the calculator. In this case, enter the pairs (1998, 1281), (1999, 1304), (2000, 1305), (2001, 1348), (2002, 1363), (2003, 1378), (2004, 1408), (2005, 1417), (2006, 1448), and (2007, 1460). Make sure to label the x-values as X and the y-values as Y.
2. Plot the points on the graphing calculator by selecting the plot function.
3. Determine the equation of the line of best fit by using the calculator's regression analysis feature. Look for the linear regression option or a similar function that calculates the equation of the line. Choose the option that provides the equation in the form of y = mx + b, where m is the slope and b is the y-intercept.
4. Round the coefficients of the equation to two decimal places.
5. The correct answer choice for the equation of the line of best fit is the one that matches the equation generated by the calculator.
6. To find the correlation coefficient, look for the option in the calculator's regression analysis that provides the correlation coefficient. It is typically denoted as r. Round the correlation coefficient to three decimal places.
Now, based on the given equation of the line of best fit, we can determine the predicted number of movie tickets sold in 2014 by substituting the year 2014 into the equation and solving for the corresponding y-value.
It appears that the options provided for the equation of the line of best fit are not accurate since the equation should have the form y = mx + b.