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Maths Gcse Wjec-Eduqas Higher

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  1. Scatter-Graphs-And-Correlation Wjec-Eduqas Higher
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  2. Cumulative-Frequency-And-Box-Plots Wjec-Eduqas Higher
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  3. Histograms Wjec-Eduqas Higher
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  4. Statistical-Diagrams- Wjec-Eduqas Higher
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  5. Averages-Ranges-And-Data Wjec-Eduqas Higher
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  6. Combined-And-Conditional-Probability Wjec-Eduqas Higher
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  7. Tree-Diagrams- Wjec-Eduqas Higher
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  8. Simple-Probability-Diagrams- Wjec-Eduqas Higher
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  9. Introduction-To-Probability Wjec-Eduqas Higher
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  10. Transformations Wjec-Eduqas Higher
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  11. Vectors Wjec-Eduqas Higher
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  12. 3D-Pythagoras-And-Trigonometry Wjec-Eduqas Higher
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  13. Sine-Cosine-Rule-And-Area-Of-Triangles- Wjec-Eduqas Higher
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  14. Pythagoras-And-Trigonometry Wjec-Eduqas Higher
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  15. Area-And-Volume-Of-Similar-Shapes Wjec-Eduqas Higher
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  16. Congruence-Similarity-And-Geometrical-Proof Wjec-Eduqas Higher
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  17. Volume-And-Surface-Area- Wjec-Eduqas Higher
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  19. Area-And-Perimeter- Wjec-Eduqas Higher
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  20. Circle-Theorems Wjec-Eduqas Higher
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  21. Bearings-Scale-Drawing-Constructions-And-Loci Wjec-Eduqas Higher
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  22. Angles-In-Polygons-And-Parallel-Lines Wjec-Eduqas Higher
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  23. Symmetry-And-Shapes Wjec-Eduqas Higher
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  24. Exchange-Rates-And-Best-Buys Wjec-Eduqas Higher
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  25. Standard-And-Compound-Units- Wjec-Eduqas Higher
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  26. Direct-And-Inverse-Proportion- Wjec-Eduqas Higher
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  27. Problem-Solving-With-Ratios Wjec-Eduqas Higher
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  28. Ratios Wjec-Eduqas Higher
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  29. Sequences Wjec-Eduqas Higher
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  30. Transformations-Of-Graphs- Wjec-Eduqas Higher
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  33. Real-Life-Graphs Wjec-Eduqas Higher
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  37. Linear-Graphs Wjec-Eduqas Higher
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  42. Coordinate-Geometry- Wjec-Eduqas Higher
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  43. Functions Wjec-Eduqas Higher
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  44. Forming-And-Solving-Equations Wjec-Eduqas Higher
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  45. Iteration Wjec-Eduqas Higher
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  47. Algebraic-Fractions- Wjec-Eduqas Higher
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  48. Completing-The-Square Wjec-Eduqas Higher
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  49. Factorising Wjec-Eduqas Higher
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  50. Expanding-Brackets Wjec-Eduqas Higher
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  51. Algebraic-Roots-And-Indices Wjec-Eduqas Higher
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  52. Introduction-To-Algebra Wjec-Eduqas Higher
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  53. Using-A-Calculator Wjec-Eduqas Higher
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  54. Surds Wjec-Eduqas Higher
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  55. Rounding-Estimation-And-Bounds Wjec-Eduqas Higher
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  56. Fractions-Decimals-And-Percentages Wjec-Eduqas Higher
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  57. Simple-And-Compound-Interest-Growth-And-Decay Wjec-Eduqas Higher
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  58. Percentages Wjec-Eduqas Higher
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  59. Fractions Wjec-Eduqas Higher
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  60. Powers-Roots-And-Standard-Form Wjec-Eduqas Higher
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  61. Prime-Factors-Hcf-And-Lcm- Wjec-Eduqas Higher
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  62. Number-Operations Wjec-Eduqas Higher
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Exam code:C300

Line of best fit

What is a line of best fit?

  • If a scatter graph suggests that there is a positive or negative correlation

    • a line of best fit can be drawn on the scatter graph

      • This can then be used to make predictions

How do I draw a line of best fit?

  • A line of best fit is drawn on by eye

    • It is a single-ruled straight line

    • It must extend across the full data set

    • It does not need to pass through any particular point(s)

    • There should roughly be as many points on either side of the line (along its whole length)

  • If there is one extreme value (outlier) that does not fit the general pattern

    • then ignore this point when drawing a line of best fit

How do I use a line of best fit?

  • Once the line of best fit is drawn, you can use it to predict values

    • E.g. to estimate y when x = 5

      • Use the line to read off the y value when x is 5

  • It is best to use your line to predict values that lie within the region covered by the data points

    • This is called interpolation

  • Be careful: if you extend your line too far away from the data points and try to predict values, those parts of the line are unreliable!

    • This is called extrapolation

Examiner Tips and Tricks

  • Sliding a ruler around a scatter graph can help to find the right position for the line of best fit!

Worked Example

Sophie wants to know if the price of a computer is related to the speed of the computer.
She tests 8 computers by running the same program on each, measuring how many seconds it takes to finish.
Sophie’s results are shown in the table below.

Price (£)

320

300

400

650

250

380

900

700

Time (secs)

3.2

5.4

4.1

2.8

5.1

4.3

2.6

3.7

(a) Draw a scatter diagram, showing the results on the axes below.

Plot each point carefully using crosses 

A scatter diagram for time against price

 (b) Write down the type of correlation shown and use it to form a suitable conclusion. 

The shape formed by the points goes from top left to bottom right (a negative gradient)
This is a negative correlation
As one quantity increases (price), the other decreases (time)

The graph shows a negative correlation
This means that the more a computer costs, the quicker it is at running the program

(c) Use a line of best fit to estimate the price of a computer that completes the task in 3.4 seconds.

First draw a line of best fit, by eye
Then draw a horizontal line from 3.4 seconds to the line of best fit
Draw a vertical line down to read off the price 

A line of best fit drawn on a scatter diagram

A computer that takes 3.4 seconds to run the program should cost around £620
A range of different answers will be accepted,
depending on the line of best fit

Responses

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