Upcoming Assignments/Quizzes

Assignments Open Time Due Time
Module 8 Data Quiz October 12th (1:00 am EST) October 14th (11:55 pm EST)
Module 6 Conceptual Quiz October 12th (1:00 am EST) October 14th (11:55 pm EST)

Notes from Discussion Board/Office Hours

Statistical Power and the p-value

There were a few questions from the previous Module about Power and it related to p-values, $$\alpha$$, $$\beta$$, and sample size. Here’s a link to a nice explainer from Khan Academy, which is also embedded in the Module 6 notes.

How to tell if assumptions are met?

In the lectures this week, Dr. Baiser demonstrated some graphical approaches for determining whether the assumptions for linear models are met. These approaches are somewhat subjective, we know what patterns we should find if the assumptions are upheld, but unlike the p-value there is no computed statistic and/or threshold for defining if the assumption is met or not. As a result, these techniques are typically much better at tell us when a model assumption does not fit than when it does.

Homoscedasticity vs. Heteroscedasticity

Homoscedasticity is a another word for the homogeneity of variance. This means that the variation we see in our response variable $$Y$$ is consistent across the range of our predictor variable $$X$$ or our predicted response $$\hat{Y}$$. This means that that if we plot the residuals against predicted values, the distance between the points should be about the same over each section of the x-axis (or the domain of $$\hat{Y}$$).

If instead we see some sort of pattern, like higher differences in one section of the graph than in another section, this would be indicative of heteroscedasticity:

Again, as we discussed earlier we’re looking for patterns, and it will typically be easier to tell of something is heteroscedastic than so be sure that it is homoscedastic. One real-world example of heteroscedastic data could be height as a function of age. Height typically increases as age increase (up to a certain), however there is a larger degree of variance in age-specific height during the pubescent years than outside this age range. I looked all over for some actual data to show this but couldn’t find any, if you find some email me and I’ll update this page.

Other notes

• Dr. Valle and I try to keep an updated list of stats and programming courses across campus, available here.
• Don’t worry, we did skip Module 7, we’ll come back to it but the subject of that module is an special type of linear model, so we decided to do this module first.
• For transforming negatively skewed data, try a Fisher transformation.
• Remember that we are checking for normality in the errors, not necessarily in the data itself.
• My office hours have moved to Tuesdays from 6:30 to 7:30 pm EST.
• Recall from our earlier module that when we set graphing parameters use par R will keep these parameters moving forward. If you’ve made a multipanel plot and want to make new single panel plots it may be helpful to “reset”" the graphing parameters by running par(mfrow = c(1,1)).
• To access the USairpollution data for the data exercises, you will have to install and load the HSAUR2
install.packages("HSAUR2")
library(HSAUR2)
SO2 temp manu popul wind precip predays
Albany 46 47.6 44 116 8.8 33.36 135
Albuquerque 11 56.8 46 244 8.9 7.77 58
Atlanta 24 61.5 368 497 9.1 48.34 115
Baltimore 47 55.0 625 905 9.6 41.31 111
Buffalo 11 47.1 391 463 12.4 36.11 166
Charleston 31 55.2 35 71 6.5 40.75 148