Interpolation & Extrapolation

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Interpolation & Extrapolation

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Interpolation & Extrapolation

  1. 1. Interpolation & Extrapolation Reading between the lines…?
  2. 2. Lesson Objectives <ul><li>The right way and the wrong way to interpret a scattergraph </li></ul><ul><li>Finding the equation of the line of best fit </li></ul><ul><li>Interpreting the straight line equation </li></ul><ul><li>Non-linear models </li></ul><ul><li>Relation and causality </li></ul>
  3. 3. Inter and Extra (-polation) Line of best fit This is INTERpolation “between” - GOOD! This is EXTRApolation “outside” - BAD!
  4. 4. Finding the Equation of the l.o.b.f. Line of best fit Draw a triangle: Measure this height Measure this base
  5. 5. 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
  6. 6. Finding the Equation of the l.o.b.f. Line of best fit Read off the y-intercept (c) h = 3 cm b = 10 cm 2.1 m = 0.3
  7. 7. Finding the Equation of the l.o.b.f. These are the key values: y = mx + c The l.o.b.f. equation is: y = 0.3 x + 2.1 2.1 m = 0.3
  8. 8. 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
  9. 9. Non-Linear Models Some shapes you need to know.
  10. 10. Non-Linear Models Exponential
  11. 11. Relation and Causality <ul><li>If there is correlation between A and B we say “A is related to B and “B is related to A” </li></ul><ul><li>This is what we mean by RELATION </li></ul><ul><li>Which one CAUSES the other one? </li></ul><ul><li>Which is the independent (control) variable and which is the dependent (response) variable? </li></ul><ul><li>This is what we mean by CAUSALITY </li></ul>
  12. 12. Relation & Causality <ul><li>Would you expect: </li></ul><ul><li>A and B to be unrelated </li></ul><ul><li>A causes B </li></ul><ul><li>B causes A ? </li></ul>A: Cigarette Consumption B: Incidence of Lung Cancer
  13. 13. Relation & Causality <ul><li>Would you expect: </li></ul><ul><li>A and B to be unrelated </li></ul><ul><li>A causes B </li></ul><ul><li>B causes A ? </li></ul>A: Number of handbags sold B: Price of handbags
  14. 14. Relation & Causality <ul><li>Would you expect: </li></ul><ul><li>A and B to be unrelated </li></ul><ul><li>A causes B </li></ul><ul><li>B causes A ? </li></ul>A: Hours spent revising B: Percentage in exam
  15. 15. Relation & Causality <ul><li>Would you expect: </li></ul><ul><li>A and B to be unrelated </li></ul><ul><li>A causes B </li></ul><ul><li>B causes A ? </li></ul>A: Hours spent playing video games B: IQ
  16. 16. Relation & Causality <ul><li>Would you expect: </li></ul><ul><li>A and B to be unrelated </li></ul><ul><li>A causes B </li></ul><ul><li>B causes A ? </li></ul>A: Parental height B: Child height
  17. 17. Relation & Causality <ul><li>Would you expect: </li></ul><ul><li>A and B to be unrelated </li></ul><ul><li>A causes B </li></ul><ul><li>B causes A ? </li></ul>A: Parental weight B: Child weight
  18. 18. Relation & Causality <ul><li>Would you expect: </li></ul><ul><li>A and B to be unrelated </li></ul><ul><li>A causes B </li></ul><ul><li>B causes A ? </li></ul>A: Standard of education B: Standard of poverty
  19. 19. Relation & Causality <ul><li>Would you expect: </li></ul><ul><li>A and B to be unrelated </li></ul><ul><li>A causes B </li></ul><ul><li>B causes A ? </li></ul>A: Standard of poverty B: Standard of health
  20. 20. Relation & Causality <ul><li>Would you expect: </li></ul><ul><li>A and B to be unrelated </li></ul><ul><li>A causes B </li></ul><ul><li>B causes A ? </li></ul>A: Standard of health B: Standard of intelligence
  21. 21. Relation & Causality <ul><li>Would you expect: </li></ul><ul><li>A and B to be unrelated </li></ul><ul><li>A causes B </li></ul><ul><li>B causes A ? </li></ul>A: Standard of intelligence B: Standard of education
  22. 22. 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?

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