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Interpolation & Extrapolation
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Interpolation & Extrapolation
Reading between the lines…?
Lesson Objectives
• The right way and the wrong way to interpret a scattergraph
• Finding the equation of the line of best fit
• Interpreting the straight line equation
• Non-linear models
• Relation and causality
Inter and Extra (-polation)
Line of best fit
This is INTERpolation “between” - GOOD!
This is EXTRApolation “outside” - BAD!
Finding the Equation of the l.o.b.f.
Line of best fit
Draw a triangle:
Measure this height
Measure this base
Finding the Equation of the l.o.b.f.
Line of best fit
Calculate the gradient:
m = h ÷ b
m = 3 ÷ 10 = 0.3 h = 3 cm
b = 10 cm
Finding the Equation of the l.o.b.f.
Line of best fit
Read off the y-intercept (c)
h = 3 cm
b = 10 cm2.1
m = 0.3
Finding the Equation of the l.o.b.f.
These are the key values:
2.1
m = 0.3
y = mx + c
The l.o.b.f. equation is: y = 0.3 x + 2.1
Interpreting y = mx + c
Age and Value of New and Used Ford Mondeo Cars
Age (years)
£The equation of the line of best fit is
y = 21000 - 3000x
So the value when new is £21000
Every year the value decreases by £3000
Non-Linear Models
Some shapes you need to know.
Non-Linear Models
y ax n b
y kax
(n 2, 1, 12)
Exponential
Relation and Causality• If there is correlation between A and B we
say “A is related to B and “B is related to A”• This is what we mean by RELATION• Which one CAUSES the other one?• Which is the independent (control) variable
and which is the dependent (response) variable?
• This is what we mean by CAUSALITY
Relation & Causality
Would you expect:
1. A and B to be unrelated
2. A causes B
3. B causes A ?
A: Cigarette Consumption
B: Incidence of Lung Cancer
Relation & Causality
Would you expect:
1. A and B to be unrelated
2. A causes B
3. B causes A ?
A: Number of handbags sold
B: Price of handbags
Relation & Causality
Would you expect:
1. A and B to be unrelated
2. A causes B
3. B causes A ?
A: Hours spent revising
B: Percentage in exam
Relation & Causality
Would you expect:
1. A and B to be unrelated
2. A causes B
3. B causes A ?
A: Hours spent playing video games
B: IQ
Relation & Causality
Would you expect:
1. A and B to be unrelated
2. A causes B
3. B causes A ?
A: Parental height
B: Child height
Relation & Causality
Would you expect:
1. A and B to be unrelated
2. A causes B
3. B causes A ?
A: Parental weight
B: Child weight
Relation & Causality
Would you expect:
1. A and B to be unrelated
2. A causes B
3. B causes A ?
A: Standard of education
B: Standard of poverty
Relation & Causality
Would you expect:
1. A and B to be unrelated
2. A causes B
3. B causes A ?
A: Standard of poverty
B: Standard of health
Relation & Causality
Would you expect:
1. A and B to be unrelated
2. A causes B
3. B causes A ?
A: Standard of health
B: Standard of intelligence
Relation & Causality
Would you expect:
1. A and B to be unrelated
2. A causes B
3. B causes A ?
A: Standard of intelligence
B: Standard of education
Relation & Causality
Think carefully about mentioning causality in your project, exam and homework answers.
In real life it is often not very simple at all.
Who said Statistics was going to be simple anyway?