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Maths Gcse Aqa Foundation

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  1. Scatter-Graphs-And-Correlation Aqa Foundation
    2 主题
  2. Statistical-Diagrams Aqa Foundation
    6 主题
  3. Averages-Ranges-And-Data Aqa Foundation
    7 主题
  4. Tree-Diagrams-And-Combined-Probability Aqa Foundation
    2 主题
  5. Simple-Probability-Diagrams Aqa Foundation
    4 主题
  6. Transformations Aqa Foundation
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  7. Vectors Aqa Foundation
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  8. Pythagoras-And-Trigonometry Aqa Foundation
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  9. Congruence-Similarity-And-Geometrical-Proof Aqa Foundation
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  10. Volume-And-Surface-Area Aqa Foundation
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  11. Circles-Arcs-And-Sectors Aqa Foundation
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  12. Area-And-Perimeter Aqa Foundation
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  13. Bearings-Scale-Drawing-Constructions-And-Loci Aqa Foundation
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  14. 2D-And-3D-Shapes Aqa Foundation
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  15. Angles-In-Polygons-And-Parallel-Lines Aqa Foundation
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  16. Symmetry-And-Shapes Aqa Foundation
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  17. Exchange-Rates-And-Best-Buys Aqa Foundation
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  18. Standard-And-Compound-Units Aqa Foundation
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  19. Direct-And-Inverse-Proportion Aqa Foundation
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  20. Ratio-Problem-Solving Aqa Foundation
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  21. Sequences Aqa Foundation
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  22. Solving-Inequalities Aqa Foundation
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  23. Real-Life-Graphs Aqa Foundation
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  24. Graphs-Of-Functions Aqa Foundation
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  25. Linear-Graphs Aqa Foundation
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  26. Coordinate-Geometry Aqa Foundation
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  27. Functions Aqa Foundation
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  28. Forming-And-Solving-Equations Aqa Foundation
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  29. Simultaneous-Equations Aqa Foundation
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  30. Solving-Quadratic-Equations Aqa Foundation
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  31. Linear-Equations Aqa Foundation
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  32. Algebraic-Reasoning Aqa Foundation
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  33. Rearranging-Formulas Aqa Foundation
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  34. Introduction Aqa Foundation
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  35. Factorising Aqa Foundation
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  36. Expanding-Brackets Aqa Foundation
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  37. Algebraic-Roots-And-Indices Aqa Foundation
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  38. Using-A-Calculator Aqa Foundation
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  39. Exact-Values Aqa Foundation
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  40. Rounding-Estimation-And-Error-Intervals Aqa Foundation
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  41. Fractions-Decimals-And-Percentages Aqa Foundation
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  42. Simple-And-Compound-Interest-Growth-And-Decay Aqa Foundation
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  43. Percentages Aqa Foundation
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  44. Fractions Aqa Foundation
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  45. Powers-Roots-And-Standard-Form Aqa Foundation
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  46. Types-Of-Number-Prime-Factors-Hcf-And-Lcm Aqa Foundation
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  47. Number-Operations Aqa Foundation
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Exam code:8300

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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