- Homework:
- Read Myers section 2.7 and do problems 2.21 and 2.24 (due next Tuesday)
- Run a simple linear regression in both JMP and Splus. Print the output. Circle everything that makes sense to you (i.e. if the Durban-Watson statistic is printed and you haven't any idea what it is, don't circle it!) Most likely, more than 1/2 of the numbers will be mysterious.

- b
_{1}is Normal(beta_{1}, sigma^{2}/S_{xx}) - c, the centercept is Normal(beta
_{0}+ beta_{1}X-bar, sigma^{2}/n) - b
_{1}and c are independent (difficult) - b
_{0}is Normal(beta_{0}, sigma^{2}(1/n + x-bar^{2}/S_{xx}))

- y-hat = c + b
_{1}(x - x-bar) - So standard error is computed in the same ways as for intercept!
- Alternative idea: shift data to make the x of interest be zero
- CI for y is y-hat +/- 2 SEs
- What does this interval forecast?

- Suppose we want to predict a future observation Y and we know x
- use above to predict E(Y|x)
- But Y - E(Y|x) has standard deviation sigma
- So prediction - Y has variance = SE(prediction)
^{2}+ sigma^{2} - What does this interval forecast?

- linear bounds
- extrapolation not any where near wide enough
- What if something doesn't lie in the prediction bounds?

- linearity (y = a + bx)
- zero mean errors (duh, how could they be anything else?)
- constant variability (homoskadastic)
- normal distribution for errors
- Independence

- goal: check all of the above assumptions

Last modified: Tue Jan 30 08:39:24 2001

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