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
Tickets Sold (millions): 1289, 1317, 1322, 1335, 1370, 1386, 1417, 1428, 1456, 1460
Using a graphing calculator to find the equation of the line of best fit and the correlation coefficient r, the equation is:
y = 5.05x + 924.27
The correlation coefficient r is 0.95.
To predict the number of movie tickets sold in 2014, we can substitute x = 2014 into the equation:
y = 5.05(2014) + 924.27
y ≈ 10212.7 + 924.27
y ≈ 11136.97
Therefore, the predicted number of movie tickets sold in 2014 is approximately 11,137 million.
The correlation coefficient r is ____
(Round to three decimal places as needed.)
The correlation coefficient r is 0.995
To find the equation of the line of best fit and the correlation coefficient for this data, we can use a graphing calculator. Here's how you can do it:
1. Input the data into your graphing calculator. Press the "Stat" or "Statistics" button on your calculator, and enter the values for "Year" into one list, and the values for "Tickets Sold" into another list.
2. Once you have entered the data, go to the graphing mode on your calculator by pressing the "Graph" or "Mode" button.
3. Select a scatterplot or scatterplot regression option from the graph settings. This will plot the given data points on a scatterplot and calculate the line of best fit for you. The options may vary depending on the calculator model, so consult your calculator's user manual if needed.
4. Once the line of best fit is plotted, the calculator should also provide you with the equation of the line. The equation will be in the form "y = mx + b," where "m" is the slope and "b" is the y-intercept. Take note of these values.
5. Next, calculate the correlation coefficient "r" by using the calculator's statistical functions. Look for an option such as "LinReg" or "LinReg(ax+b)" in your calculator's statistics menu. Select this option and enter the two lists of data. The correlation coefficient "r" will be displayed on the screen.
To predict the number of movie tickets sold in 2014:
6. Substitute the year "2014" into the equation of the line of best fit that you obtained earlier to find the corresponding predicted value of tickets sold.
Using these steps, you should be able to find the equation of the line of best fit, determine the correlation coefficient "r," and predict the number of movie tickets sold in 2014.