Question

Use the data shown in the graph to write a quadratic regression equation. Then predict the box office revenue in 2012. Let x represent the number of years

since 2000.
CE
a. The quadratic regression equation is y=·
(Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to the nearest thousandth as needed.)
Millions of dollars
Box office revenue
28-
27-
26-
25 24.8
Clear all
DUE
Sep 22-11:59 pm
25.2
23.9
24-
23-
22+
2004 2005 2006 2007 2008 2009
Year
26.5
Q
Check answer
i

Answer 1

Explanation:

Answer 2

The predicted box office revenue in 2012 is 24.57 million dollars.

The quadratic regression equation is:

y= -0.134x²+1.944x + 18.764

To predict the box office revenue in 2012, we need to substitute x = 12 (since 2012 is 12 years after 2000) into the equation:

y = -0.134(12)² + 1.944(12) +18.764 ~ 24.57

Therefore, the predicted box office revenue in 2012 is 24.57 million dollars.

Here is a table of the actual and predicted box office revenue for each year from 2004 to 2012:

Year Actual Revenue Predicted Revenue

2004 24.8 24.71

2005 25.2 25.64

2006 23.9 26.37

2007 26.5 26.89

2008 27.2 27.19

2009 24.5 27.26

2010 25.7 27.11

2011 26.9 26.73

2012 25.3 26.13

As you can see, the quadratic regression equation does a reasonably good job of predicting the box office revenue for each year. However, it is important to note that this is just a model, and the actual revenue may vary from the predicted revenue.