Jackie Scheiber RADMASTE Wits University Jackie.scheiber@wits.ac.za

1. Using a calculator to investigate whether a linear, quadratic or exponential function best fits a set of bivariate numerical data Jackie Scheiber RADMASTE Wits University Jackie.scheiber@wits.ac.za

2. Curriculum References

4. Bivariate Data • BIVARIATE DATA – each item in the population has TWO measurements associated with it • We can plot bivariate data on a SCATTER PLOT (or scatter diagram or scatter graph or scatter chart) • The scatter graph shows whether there is an association or CORRELATION between the two variables

5. Some Types of Correlation

6. TASK 1

7. 1)

8. 2) • Negative correlation • As the date increases, the time taken decreases

9. 3 a) A = 23,746 … ≈ 23,75 B = - 0,0069… ≈ - 0,007 Equation of the linear regression line is y = 23,75 – 0,007 x

10. 3 b)

11. 3 c)

12. 4 a) A = - 418,943 … ≈ - 418,94 B = 0,439 … ≈ 0,44 C = - 0,00011 … ≈ - 0,001 Equation of the quadratic regression function: y = - 418,94 + 0,44 x – 0,0001 x2

13. 4b)

14. 4 c)

15. 5 a) A = 40,294 … ≈ 40,29 B = 0,9992… ≈ 0,999 Equation of the exponential regression function: y = 40,29 . (0,999)x

16. 5 b)

17. 5 c)

18. 6)

19. 7)

20. 7) continued • Compare the Linear and Exponential regression functions – similar results – rather use the straight line as it is simpler • Compare the Linear and Quadratic regression functions – similar results – but part of the data may appear quadratic, but the entire set may be less symmetric. • The Linear regression function seems to suit the given data best.

21. TASK 2

22. 1)

23. 2) • y = 69,14 + 0,06 x • y = 75,39 . (1,0004)x

24. 3)

25. 4)

26. 5) • As can be seen in the table, each time the values from the linear model are closest to the measured values – so the linear model fits the data better.