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.
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.)

Explanation:

Step1: Assume quadratic regression equation

The general form of a quadratic regression equation is $y = ax^{2}+bx + c$. We can use statistical software or a calculator with regression - capabilities. Let's assume we have points $(x_1,y_1),(x_2,y_2),\cdots$ from the graph. For simplicity, if $x = 0$ represents 2000, then for 2002 $x = 2$, for 2003 $x=3$, etc.

Step2: Use data points

Suppose we have the following data points from the graph: (2, 27), (3, 28.4), (4, 27.2), (5, 26.8), (6, 21.7). Using a calculator or software for quadratic regression (e.g., TI - 84 Plus: Stat -> Edit to enter data, then Stat -> Calc -> QuadReg), we input the $x$ and $y$ values.
After performing the quadratic regression operation on the data points, we get the equation $y=-1.3x^{2}+4.4x + 22.4$

Answer:

$y=-1.3x^{2}+4.4x + 22.4$