1. Stats for Engineers Lecture 9

2. Summary From Last Time Confidence Intervals for the mean t-tables Q Student t-distribution

3. Sample size How many random samples do you need to reach desired level of precision? Want Need:

4. Answer: Assuming plates have independent weights with a Normal distribution i.e. need to test about 28

5. 1.88.5 2.280 3.2800 4.28000

6. Linear regression

8. e.g.

9. 1.2. 3. 4.

10. e.g.

11. Or is it What do we mean by a line being a ‘good fit’?

12. Simple model for data: Random errorStraight line - Linear regression model

13. Maximum likelihood estimate = least -squares estimate Minimize Data pointStraight-line prediction E is defined and can be minimized even when errors not Normal – least-squares is simple general prescription for fitting a straight line (but statistical interpretation in general less clear) Want to estimate parameters a and b, using the data.

14. Question from Derek Bruff 1. 2. 3. 4.

15. Where Sample means Equation of the fitted line is

16. Most of the things you need to use are on the formula sheet

18. y2401811931551721101137594 x1.69.415.520.022.035.543.040.533.0 Example: The data y has been observed for various values of x, as follows: Fit the simple linear regression model using least squares. Answer:

20. Which of the following data are likely to be most appropriately modelled using a linear regression model? 1. 2. 3.

21. [derivation in notes] Quantifying the goodness of the fit Residual sum of squares

22. Question from Derek Bruff 1. 2. 3.