Stat 217 – Day 27 Topics in Regression

Last Time – Inference for Regression Ho: no association or  =0 Ha: is an/positive/negative association Minitab output  t test statistic from “coefficient of x” row  two-sided p-value  SE(b) = amount of random variation of slopes from sample to sample Strength of evidence (p-value) vs. strength of association (r) P. 605

Example 2: Textbook prices The relationship between textbook price and number of pages appears stronger than between textbook prices and year of pub. Every time the pages are increased by one the predicted price will increase by $.147. The p-value is (t = 7.65) so I would reject the null hypothesis. Strong evidence there is an association between pages in textbook and price (in the population).

Example 1: Gesell data Can we predict later intelligence based on when the child first speaks?

Removing the one child has a pretty big impact on the regression line, significance Example 1: Gesell data

Best conclusion?  Some evidence that children who take a particularly long time to speak may have lower IQ scores, but otherwise no relationship between age of first words and later IQ.  For children who take between 5 and 20 months, no relationship…

In fact 42 months and Gesell = 120 Regression line follows that one child!

Example 1: Gesell data 15 months and Gesell = 57

Influential Observations Observations whose removal has a dramatic impact on the regression line (or p-value or correlation coefficient) Most likely candidates – extreme x values

Example 2: FEV

To Turn in with partner For Wednesday  Lab 9  Start bringing review questions  (Thursday in lab – case study type worksheet)