Question

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
Full Service 81
1999
102
2000
2001
122
111
Fast Food
98
107
109
114
2002
128
118
122
2004
143
2003
136
125
a) Write a linear regression equation for the "full service" restaurant.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To write a linear regression equation for the "full service" restaurant, we need to determine the slope and y-intercept.

First, we need to calculate the slope (m) using the formula:

m = (change in y) / (change in x)

For the years 1995 to 2004, the change in x is 9 (2004-1995) and the change in y is 143 - 81 = 62.

So, the slope (m) is:

m = 62 / 9 ≈ 6.889

Next, we need to determine the y-intercept (b). We can choose any point from the data to plug into the equation once we have b.

Let's choose the point (0, 81) for our calculations.

Using the slope-intercept form of the linear regression equation:

y = mx + b

81 = 6.889 * 0 + b
81 = b

So, the y-intercept (b) is 81.

Now we can write the linear regression equation for the "full service" restaurant:

y = 6.889x + 81