Line of best fit - Teacher Slides.pptx

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Line of best fit

Interpreting and representing data

Lesson 4 of 6

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Last Lesson

Interpreting and representing data

Lesson 4 of 6

Answer each one, then check.

1

What does positive correlation mean?

2

What is an outlier?

3

Does correlation prove that one thing causes another?

4

Which correlation: temperature and hot drinks sold?

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Last Lesson - Answers

Interpreting and representing data

Lesson 4 of 6

1

What does positive correlation mean?

As one value increases, the other increases.

2

What is an outlier?

A value that does not fit the pattern.

3

Does correlation prove that one thing causes another?

No

4

Which correlation: temperature and hot drinks sold?

Negative

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Learning Objectives

Interpreting and representing data

Lesson 4 of 6

1

Draw a line of best fit on a scatter graph.

2

Use a line of best fit to estimate values (interpolation).

3

Explain why extrapolation can be unreliable.

4

Decide how reliable an estimate is.

5

Deal with outliers when drawing a line of best fit.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Drawing a Line of Best Fit

Interpreting and representing data

Lesson 4 of 6

A line of best fit is a single straight line that follows the trend of the points.

Straight, with a ruler

One straight line - not a curve, and not dot to dot.

Through the middle

About the same number of points on each side, following the slope of the pattern.

Ignore outliers

An outlier would pull the line away from the rest.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Drawing a Line of Best Fit (cont.)

Interpreting and representing data

Lesson 4 of 6

Not always from 0

The line does not have to go through the origin.

Only with correlation

If there is no correlation, there is no line of best fit.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

A Line of Best Fit in Use

Interpreting and representing data

Lesson 4 of 6

Up from 4.5 years, across to about £6700.

To estimate a value, go from the known value to the line of best fit, then across to the other axis. Here, a car 4.5 years old is estimated to be worth about £6700. The estimate is reasonable because 4.5 years is inside the range of the data.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Interpolation and Extrapolation

Interpreting and representing data

Lesson 4 of 6

INTERPOLATION - INSIDE THE DATA

• Estimating within the range of values you have.

• A 4.5-year-old car, when the data covers 1 to 8 years.

• Usually reliable, if the correlation is strong.

EXTRAPOLATION - OUTSIDE THE DATA

• Estimating beyond the range of values you have.

• A 15-year-old car, when the data stops at 8 years.

• Unreliable: the pattern may not continue - the line would say the car is worth less than nothing.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Using a Line of Best Fit

Interpreting and representing data

Lesson 4 of 6

Use the car graph to estimate (a) the value of a car that is 4.5 years old, and (b) the age of a car worth £9000.

1

(a) Go up from 4.5 on the age axis to the line

then across to the value axis

2

Read the value

about 6.7 (£ thousands)

3

(b) Go across from 9 on the value axis to the line

then down to the age axis

4

Read the age

about 2.8 years

ANSWER

(a) About £6700 (b) About 2.8 years (accept answers close to these)

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How Reliable Is the Estimate?

Interpreting and representing data

Lesson 4 of 6

An estimate from a line of best fit is only as good as the data behind it.

Strong correlation

Points close to the line give more reliable estimates.

Inside the data

Interpolation is more reliable than extrapolation.

Enough data

Estimates from 30 points are more reliable than from 5.

Sensible values

A line might predict a negative price or a test score over 100 - a sign it has gone too far.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Key Terms

Interpreting and representing data

Lesson 4 of 6

Line of best fit

A straight line drawn through the middle of the points on a scatter graph, following the trend.

Interpolation

Estimating a value inside the range of the data.

Extrapolation

Estimating a value outside the range of the data.

Reliable

Likely to be accurate.

Outlier

A point that does not fit the pattern, ignored when drawing the line.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Interpreting and representing data

Lesson 4 of 6

YOUR TASK

Plot, Fit, Estimate

15 minutes

Ten students recorded their arm span and height, in cm: (150, 152), (155, 154), (158, 160), (162, 161), (165, 167), (168, 166), (171, 172), (175, 174), (178, 180), (182, 181). Plot a scatter graph, draw a line of best fit, estimate the height of a student with an arm span of 173 cm, and explain whether you could use the graph for an adult with an arm span of 200 cm.

1

Choose sensible scales and label the axes.

2

Plot the points and draw the line.

3

Estimate, and comment on reliability.

WHAT A GOOD ANSWER SHOWS

Strong positive correlation; the line is close to height = arm span. Estimate for 173 cm: about 173 cm. An arm span of 200 cm is outside the data (extrapolation), so the estimate would be less reliable.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Can I...?

Interpreting and representing data

Lesson 4 of 6

Draw a line of best fit.

Leave out outliers when drawing it.

Estimate a y-value from an x-value.

Estimate an x-value from a y-value.

Explain interpolation.

Explain extrapolation.

Say why an estimate might be unreliable.

Spot an estimate that makes no sense.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Summary & Exam Focus

One straight line through the middle of the points, ignoring outliers.

Up (or across) to the line, then across (or down) to read the estimate.

Interpolation is inside the data and usually reliable; extrapolation is outside it and often not.

Stronger correlation and more data give more reliable estimates.

EXAM FOCUS

Explain why it may not be sensible to use the line of best fit to estimate the score of a student who revised for 20 hours. (1 mark)

When asked to estimate from a graph, draw the lines you use on the graph. An answer in the accepted range earns the marks, and the lines show the examiner your method.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Exam Practice: Line of Best Fit

Interpreting and representing data

Lesson 4 of 6

Answer all questions. Draw any lines you use on the graph. · 15 minutes

Question 1 · 5 marks · Calculator

The scatter graph shows the number of hours ten students revised and their test scores. (a) One point is an outlier. Write down its…

Question 2 · 1 mark · Calculator

What is the difference between interpolation and extrapolation?

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Question 1 · 5 marks · Calculator

Interpreting and representing data

Lesson 4 of 6

The scatter graph shows the number of hours ten students revised and their test scores. (a) One point is an outlier. Write down its coordinates. (b) Draw a line of best fit on the graph. (c) Use your line to estimate the score of a student who revised for 5.5 hours. (d) Explain why it may not be… (5 marks)

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Question 1 · mark scheme

Interpreting and representing data

Lesson 4 of 6

5 marks available. Award a mark for each point made.

(a) (3, 85)

B1

(b) A single straight line within the band of the points, ignoring the outlier

B1

(c) Reading from their line at 5.5 hours

M1

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Question 1 · mark scheme (cont.)

Interpreting and representing data

Lesson 4 of 6

(c) An answer in the range 57 to 63

A1

(d) A reason such as outside the range of the data, or the score cannot exceed 100

C1

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Question 2 · 1 mark · Calculator

Interpreting and representing data

Lesson 4 of 6

“

What is the difference between interpolation and extrapolation?

HOW TO ANSWER IT

Command word: Calculator. Worth 1 mark, so plan before writing.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Question 2 · mark scheme

Interpreting and representing data

Lesson 4 of 6

1 mark available. Award a mark for each point made.

Both described correctly

B1

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