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 91 116 134 144 149 155 159
Fast Food 109 118 120 126 131 134 139
Question content area bottom Part 1 a) Write a linear regression equation for the "full service" 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 "full service" restaurant, we need to find the equation of a straight line that best fits the given data points.
Let's assume that the linear regression equation is of the form y = mx + b, where y represents the revenue of the "full service" restaurant in billions of dollars, and x represents the year (with x=0 representing the year 1990).
We can use the given data points to find the slope (m) and y-intercept (b) of the line.
Using the two points (x1, y1) = (0, 91) and (x2, y2) = (14, 159), we can find the slope (m) as:
m = (y2 - y1) / (x2 - x1)
m = (159 - 91) / (14 - 0)
m = 68 / 14
m = 4.857
Now, we can substitute one of the points into the linear equation to find the y-intercept (b). Let's use the point (0, 91):
91 = 4.857(0) + b
91 = b
Hence, the y-intercept (b) is 91.
Therefore, the linear regression equation for the "full service" restaurant is:
y = 4.857x + 91