1. Lesson # 6: Identifying relations
May 19, 2011

2. A linear regression is used to determine the line of best fit for linear relations and data.
In the same way, both quadratic and exponential regressions can be performed for corresponding relations or data.

3. Linear Relations
y= mx + b
- First differences are constant
between consecutive terms
- Straight line

4. Quadratic Relations
y = ax2 + bx + c
- Second differences are constant
between consecutive terms
- Smooth curve with a steady change

5. Exponential Relations
y = abx
There is a constant rate/ratio between
consecutive terms
- Smooth curve with a rapid change

6. EXAMPLE 1: Identify the type of relation
(and explain how you know what type it is) a)
Time (s) 20 40 60 80
100
120
140
Height (m)
130
105 83 64 48 35 25 18
First differences: -25, -22, -19, -16, -13, -10, -7
Second Differences: 3, 3, 3, 3, 3, 3
Quadratic relation – Second differences are constant

7. Linear relation- First differences are constantb)
Time (min) 10 20 30 40 50 60 70
Volume (L) 69 78 87 96
105
114
123
First Differences: 9, 9, 9, 9, 9, 9, 9
Linear relation- First differences are constant

8. First Differences: -768, -382, -192 (not constant)
Time to see effect (hours) 8 7 6 5 4 3 2 1
Dose of medication (mL)
1536
768
384
192 96 48 24 12
First Differences: -768, -382, -192 (not constant)
Second Differences: 386, 190 (not constant)
Ratios: 0.5, 0.5, 0.5, 0.5, 0.5, 0.5
Exponential relation – Ratios are constant
Complete: Pg 323 # 1 – 4
Assignment: Pg 324 # 6, 9 ab