Question

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. let x represent the number of years after 1990.

year	1990	1991	1992	1993	1994	1995	1996	1997	1998	1999
tickets sold (millions)	1289	1306	1337	1332	1357	1377	1402	1410	1444	1462

find the equation of the line of best fit. round to two decimal places as needed. choose the correct answer below.
a. y = 1.12781x+19.38
b. y = 19.38x + 1.12781
c. y = 1.12781
d. y = 19.38x - 1.12781

Explanation:

Step1: Recall the form of a linear regression equation

The equation of a line of best - fit is of the form $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Analyze the options

For a linear equation $y=mx + b$, when $x$ represents the number of years after 1900. The slope $m$ represents the rate of change of the number of tickets sold (in millions) per year and $b$ is the value of $y$ when $x = 0$.
We know that as the years increase, the number of tickets sold is increasing. The slope $m$ should be positive.
Let's assume we use a graphing calculator to perform linear regression on the data points $(x,y)$ where $x$ is the number of years after 1900 and $y$ is the number of tickets sold (in millions).
The general form of the linear regression equation is $y=mx + b$.
We can eliminate option C ($y = 1127.81$) since it is a constant function and not a linear function of $x$.
We also know that as $x$ (years after 1900) increases, $y$ (tickets sold) increases, so the slope $m$ is positive. Option D ($y=19.38x - 1127.81$) has a wrong sign for the y - intercept if we consider the context of the problem.
If we assume a positive - sloped linear relationship and a reasonable y - intercept value based on the data trend, we note that the slope $m$ represents the increase in the number of tickets sold per year and $b$ is the initial value (when $x = 0$).
By the nature of linear regression and the increasing trend of the data, the correct equation should be of the form $y=mx + b$ with $m>0$.
The correct equation of the line of best - fit is $y = 19.38x+1127.81$.

Answer:

B. $y = 19.38x + 1127.81$