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

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 $\mathrm {R} ^{2}$ for each:

(a) ${\hat {y}}=\beta _{0}+\beta _{1}x+\varepsilon$

(b) ${\hat {y}}=\beta _{0}+\beta _{1}x+\beta _{2}i+\beta _{3}j+\varepsilon$

(c) ${\hat {y}}=\beta _{0}+\beta _{1}x+\beta _{2}i+\beta _{3}j+\beta k+\varepsilon$

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 your table.

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) ${\widehat {\mathrm {fruit} }}=\beta _{0}+\beta _{1}\mathrm {obama} +\varepsilon$

(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.