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 3 problem set's programming challenges