In the United States, the revenue (money taken from sales) at a "full service" restaurant is increasing at a faster rate than the revenue at a "fast food" restaurant. The data below represent the annual revenue in billions of dollars for each type of restaurant. Use the data to answer the three questions below. Let x=0 represent the year 1990.
Year 1995 1999 2000 2001 2002 2003 2004
Full Service 82 111 124 131 139 146 156
Fast Food 107 111 113 118 120 124 127
Part 2 b) Now write a linear regression equation for the "fast food" restaurant. y=enter your response here (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.)
To write a linear regression equation for the "fast food" restaurant, we need to find the equation of a straight line that best fits the data points.
Let's denote the independent variable (x-axis) as the number of years since 1990: x = 0 represents the year 1990.
The given data points for the "fast food" restaurant are:
(0, 107), (4, 111), (5, 113), (6, 118), (7, 120), (8, 124), (9, 127)
Using these points, we can calculate the equation of the line using the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
First, let's calculate the slope (m):
m = (y2 - y1) / (x2 - x1)
m = (111 - 107) / (4 - 0)
m = 4 / 4
m = 1
Now, let's substitute one of the points (0, 107) and the slope (m) into the equation and solve for b:
107 = 1(0) + b
b = 107
Therefore, the linear regression equation for the "fast food" restaurant is:
y = 1x + 107
Simplifying the equation, we get:
y = x + 107