Answer: If the relationship between fuel efficiency (L/100 km) and liters used is linear, we would expect the first differences to be constant. In a linear relationship, the rate of change (or slope) remains constant throughout the data points.
First differences are calculated by taking the difference between consecutive data points in the sequence. If the first differences are constant, it means that the change in fuel efficiency (L/100 km) between any two data points is consistent.
For example, let's say we have the following data points for fuel efficiency (L/100 km) and liters used:
Fuel Efficiency (L/100 km) Liters Used
10 10
8 12
6 14
4 16
To calculate the first differences, we subtract each consecutive data point from the previous one:
First Difference (Fuel Efficiency): 10 - 8 = 2
First Difference (Fuel Efficiency): 8 - 6 = 2
First Difference (Fuel Efficiency): 6 - 4 = 2
As you can see, the first differences for fuel efficiency are all 2. This indicates a linear relationship between fuel efficiency and liters used, as the rate of change in fuel efficiency is consistent (2 L/100 km) between any two data points.