Question

use the data shown in the graph to write a quadratic regression equation. then predict the box office revenue in 2013. 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: Recall quadratic regression formula

A quadratic regression equation has the form $y = ax^{2}+bx + c$. Usually, we use statistical software or a graph - ing calculator with regression capabilities to find the values of $a$, $b$, and $c$ based on the data points. Since the data points from the graph are not explicitly given in a numerical list, we assume a general approach. If we were to use a calculator or software, we would input the data pairs (where $x$ is the number of years since 2000 and $y$ is the box - office revenue in millions of dollars).
However, without the actual data - entry process, we can't calculate the exact values. But for the sake of showing the process, if we had data points $(x_1,y_1),(x_2,y_2),\cdots,(x_n,y_n)$, we would set up a system of equations based on the least - squares method to solve for $a$, $b$, and $c$.
Let's assume we use a graphing utility to perform the quadratic regression on the data from the graph.

Step2: Interpret the result

After using the graphing utility or software to perform the quadratic regression on the data points from the graph, we get the values of $a$, $b$, and $c$.
Since we have no access to the actual data points from the graph for calculation, we can't provide the exact equation. But if we assume we have done the regression correctly, the equation will be in the form $y=ax^{2}+bx + c$.

Since we don't have the data to calculate the actual values of $a$, $b$, and $c$, we can't give a specific answer. If we had the data points:
Let the data points be $(x_i,y_i)$ for $i = 1,\cdots,n$. We know that the sum of the squared errors $S=\sum_{i = 1}^{n}(y_i-(ax_{i}^{2}+bx_i + c))^{2}$ is minimized. By taking partial derivatives of $S$ with respect to $a$, $b$, and $c$ and setting them equal to zero, we get a system of linear equations to solve for $a$, $b$, and $c$.

If we assume we have used a graphing calculator or software to perform the regression on the data from the graph:
Let's say the calculator gives us $a=- 0.5$, $b = 3$, $c=25$ (these are just example values). The quadratic regression equation would be $y=-0.5x^{2}+3x + 25$.

In a real - world scenario, we would input the data from the graph (the $x$ values representing years since 2000 and $y$ values representing box - office revenue) into a statistical tool to get the correct values.

Since we don't have the actual data for calculation, we can't provide a definite answer. But if we assume we have calculated it correctly using the data from the graph, the answer will be in the form $y = ax^{2}+bx + c$.

Answer:

We need the actual data points from the graph to calculate the quadratic regression equation. Without them, we cannot provide a specific answer.