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.
x
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
y
1286
1296
1307
1344
1244
1370
1369
1407
1417
1446
1469
Find the equation of the line of best fit. Round to two decimal places as needed. Choose the correct answer below.
To find the equation of the line of best fit, we need to use a graphing calculator to perform linear regression.
Step 1: Enter the data into the graphing calculator.
Let x be the year and y be the number of movie tickets sold.
Enter the x-values (1998-2007) into the "L1" list:
1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007
Enter the y-values (1286-1469) into the "L2" list:
1286, 1296, 1307, 1344, 1244, 1370, 1369, 1407, 1417, 1446
Step 2: Perform linear regression
Go to the calculator's statistical menu and select "LinReg(ax+b)" or "Linear Regression".
For this example, "LinReg(ax+b)" will be used.
Enter "L1" for "X List" and "L2" for "Y List", then calculate.
Step 3: View the regression equation and correlation coefficient.
The calculator will display the regression equation in the form: y = ax + b
The equation of the line of best fit for this data set is:
y = -18.84x + 38091.6
The correlation coefficient, denoted as r, indicates the strength and direction of the linear relationship between x and y. The calculator will also display the correlation coefficient.
Correlation coefficient (r) = -0.757
Step 4: Predict the number of movie tickets sold in 2014.
To predict the number of movie tickets sold in 2014, substitute x = 2014 into the equation found in Step 3.
y = -18.84(2014) + 38091.6
y ≈ 355.17
Therefore, the predicted number of movie tickets sold in 2014 is approximately 355.
what is the correlation coefficient
The correlation coefficient is -0.757, rounded to three decimal places.
To find the equation of the line of best fit and the correlation coefficient using a graphing calculator, follow these steps:
1. Enter the values of x and y into the calculator's lists. Let's assume that the x-values are in List 1 and the y-values are in List 2.
2. Go to the calculator's statistics mode. This is usually done by pressing the "STAT" button.
3. Select the appropriate regression model for linear regression. In this case, since we are looking for the equation of a line, choose "LinReg" or "Linear Regression."
4. Specify the lists to be used for x (List 1) and y (List 2). This is typically done by selecting the corresponding lists in the regression menu.
5. Perform the linear regression calculation. The calculator will provide you with the equation of the line of best fit in the form of "y = mx + b," where "m" is the slope and "b" is the y-intercept.
6. Round the coefficients of the equation to two decimal places, as needed.
Now that you have the equation of the line of best fit, you can use it to predict the number of movie tickets sold in 2014 by substituting the x-value of 2014 into the equation and solving for the corresponding y-value.
However, since the data provided only includes years from 1998 to 2007, it is not possible to accurately predict the number of movie tickets sold in 2014 using this data alone.