The linear regression equation for a Fast Full Service restaurant is y = 6.612x + 62.819
The linear regression equation for a Fast Food restaurant is y = 3.197x + 90.777
Let x = 0 represent the 1990. Find the year where the two types of restaurants was the same. Round to the nearest year as needed.
Year 1995 1999 2000 2001 2002 2003 2004
Full Service 97 118 128 140 144 147 155
Fast Food 110 116 119 126 130 134 137
To find the year where the two types of restaurants had the same number of customers, we need to find the x-coordinate where the two regression lines intersect.
Setting the two regression equations equal to each other:
6.612x + 62.819 = 3.197x + 90.777
Simplifying the equation:
6.612x - 3.197x = 90.777 - 62.819
3.415x = 27.958
x = 27.958 / 3.415
x ≈ 8.17
Since x represents the number of years after 1990, we can round x to the nearest year:
x ≈ 8 years
Adding 8 years to 1990:
1990 + 8 = 1998
Therefore, the two types of restaurants had the same number of customers in the year 1998.