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?