# Statistics and Statistical Programming (Winter 2017)/Problem Set: Week 8

## Programming Challenges

The first set of programming challenges will use your the individual dataset we used in the week 3 problem set's programming challenges:

PC0. Load up your dataset as you did in Week 3 PC2.
PC1. If you recall from Week PC6, x and y seemed like they linearly related. We now have the tools and terminology to describe this relationship and to estimate just how related they are. Run a t.test between x and y in the dataset and be ready to interpret the results for the class.
PC2. Estimate how correlated x and y are with each other.
PC3. Recode your data in the way that I laid out in Week 3 PC7.
PC4. Generate a set of three linear models and be ready to intrepret the coefficients, standard errors, t-statistics, p-values, and ${\displaystyle \mathrm {R} ^{2}}$ for each:
(a) ${\displaystyle {\hat {y}}=\beta _{0}+\beta _{1}x+\varepsilon }$
(b) ${\displaystyle {\hat {y}}=\beta _{0}+\beta _{1}x+\beta _{2}i+\beta _{3}j+\varepsilon }$
(c) ${\displaystyle {\hat {y}}=\beta _{0}+\beta _{1}x+\beta _{2}i+\beta _{3}j+\beta k+\varepsilon }$
PC5. Generate a set of residual plots for the final model (c) and be ready to interpret your model in terms of each of these:
(a) A histogram of the residuals.
(b) Plot the residuals by your values of x, i, j, and k (four different plots).
(c) A QQ plot to evaluate the normality of residuals assumption.
PC6. Generate a nice looking publication-ready table with a series of fitted models and put them in a Word document.

Now, lets go back to the Michelle Obama dataset we used last week the week 7 problem set's programming challenges.

PC7. Load up the dataset once again and fit the following linear models and be ready to interpret them similar to the way you did above in PC4:
(a) ${\displaystyle {\widehat {\mathrm {fruit} }}=\beta _{0}+\beta _{1}\mathrm {obama} +\varepsilon }$
(b) Add a control for age and a categorical version of a control for year to the model in (a).
PC8. Take a look at the residuals for your model in (a) and try to interpret these as you would in PC4 above. What do you notice?
PC9. Run the simple model in (a) three times on three subsets of the dataset: just 2012, 2014, and 2015. Be ready to talk through the results.

## Statistics Questions

Q0. Any questions or clarifications from the PSU material or the OpenIntro text?
Q1-Q4. The next four questions are all of the form "interpret this model" and are using the example we used in the text. They are listed on this page I've created (it requires a UW NetID). If it's helpful, that page also includes all the R code so you can try stuff out yourself.
Q5. Exercise 8.16 on Challenger o-rings.
Q6. Exercise 8.18 which is more on challenger o-rings.

## Empirical Paper Questions

These questions are about the Lampe and Resnick once again. For this week, we'll focus on the logistic regression table in Table 4.

Q7. Be ready to explain what Table 4 means in both statistical and substantive terms. In particular, be ready to interpret the coefficients in substantive terms and be ready to explain what the Z-statistics, Pseudo ${\displaystyle R^{2}}$, and p-values mean. Be ready to provide an sentence for each that interprets each number in the table in substantive terms. This will mean understanding what every variable actually measures.

## Questions on Ioannidis (2005)

Q8. Be ready to summarize the main point of, and share some reflections on, the paper. There are no specific questions.