Chapter 14: Inference about the Model

Confidence Intervals for the Regression Slope (p. 788) If we repeated our sampling and computed another model, would we expect a and b to be exactly the same? – Of course not, given what we’ve learned about random variation and sampling error! We are interested in the true slope (β), which is unknowable, but we are able to estimate it. Confidence Interval for the slope β of the true regression line: Given in output from stats package.

Is β=0? H 0 : β=0 vs. H a : β ≠0 or β>0 or β<0 Perform a t-test:

Example See Figure 14.1, p. 782 – Count of crying peaks vs. IQ Now, see Figure 14.4, p. 790

Example, cont.

Four Items of Interest Model: estimate of α and β. Standard deviation about the line of best fit. – The higher the value, the higher the spread about the regression line. C.I. for β – Need SE b Significance test for H 0 : β=0 – t=b/SE b

Practice Exercise 14.6, p. 794 Look at 2002 MC #21

Homework Free Response Problems: – #2, 2006 – #6, 2007