1. Regression Wisdom Chapter 9 - continued

2. Warm-up: Remember this??? Suppose a Normal model describes the number of pages printer ink cartridges last. If we keep track of printed pages for the 47 printers at a company's office, which must be true? I. The page counts for those ink cartridges will be normally distributed. II. The Histogram for those page counts will be symmetric. III. 95% of those page counts will be within 2 standard deviations of the mean. a) None b) I only c) II only d) II and II e) I, II, and III

3. Warm-up: Remember this??? Suppose a Normal model describes the number of pages printer ink cartridges last. If we keep track of printed pages for the 47 printers at a company's office, which must be true? I. The page counts for those ink cartridges will be normally distributed. II. The Histogram for those page counts will be symmetric. III. 95% of those page counts will be within 2 standard deviations of the mean. a) None b) I only c) II only d) II and II e) I, II, and III

4. From the listserv questioner…”The answer is that none of those statements are true. Is this because of the certainty in the statements??” Answer from Dave Bock (co-author of your text book)…”Yes. Models estimate what might happen; they cannot guarantee what will happen. We see this kind of misunderstanding frequently in student responses on the AP exam.”

5. From the listserv questioner…”The answer is that none of those statements are true. Is this because of the certainty in the statements??” Answer from Corey Andreasen, another one of the experts…”Yes. You have a sample of 47 printers, so even if a normal model is highly accurate for the population of all printer cartridges, this sample a. cannot be normal. It will be a discrete distribution. May be approximately normal, but that's not what was stated. b. may or may not have a symmetric histogram. Probably will have a roughly symmetric histogram, but MUST c. will probably not have exactly 95% of the counts within two standard deviations of the mean. Unsure? What's 95% of 47?”

6. Homework questions ????

7. Regression Wisdom Take caution with averaged data

8. What do you think…?? correlations using averaged data A plot of the average height of young children against their age in months would give a strong positive correlation.  Given the age and height data on 20 individual young children, would the correlation be higher or lower?

9. Many regression or correlation studies work with averages that combine information from many individuals. Averages will not have the amount of variation that individual values do---that is, plots of individuals will show much more ‘scatter’.

10. Correlation based on averages are usually too high when applied to individuals….Another reminder that it is important to note exactly what variables were measured. ** Be suspicious of conclusions based on regressions of summary data—they may look better than they really are.

11. Example: The data set in the table is taken from The Data and Story Library. Researchers measured the heights of 161 children in Kalama, a village in Egypt. The heights were averaged and recorded each month, with the study lasting several years. The data is presented in the table that follows.The Data and Story Library Age (months)Mean Height (cm) 1876.1 1977 2078.1 2178.2 2278.8 2379.7 2479.9 2581.1 2681.2 2781.8 2882.8 2983.5

12. Mean Height versus Age

13. Data of Individual age vs. height measurements (not from same study)

14. Matching Descriptions to Scatterplots handout