Re-sampling methods

1. Simulations.
(a) Simulate an experiment of rolling a die 200 times. Picture the frequencies (outcomes) in a histogram.
(b) Replicate la for rolling 1000 times to estimate the probability of obtaining even numbers in each replication and print its histogram.
(c) Simulate an experiment of rolling two dices together 1000 times, estimate the probability that sum of them are 6, and plot how these estimates converge from rolling 10 to 1000 times.

Regression

2. For this question you need the 2007 Airline data
(a) Import the data as an ff data frame (for this you will need the packages ff and ffbase).
(b) Take a subset of the data for the month February. Henceforth you will use this subset for the analysis. This should not be so big that you cannot fit it in the memory, so you can work with the traditional functions in R (e.g. lm()).
(c) If you have the subset in a ff data. frame make it into a traditional R data.frame and show that your data object actually is a R data.frame.
(d) Obtain the sample size of this data.
(e) Run a regression with the following formula: ActualElapsedTime -DayOfWeek+UniqueCarrier+Distance
(f) What is the predicted average travel time for Rob who is going to travel 500 miles, next Friday with Pinnacle Airlines Inc. (9E)?
(g) What is the predicted average travel time for Anna who is going to make the same trip as Rob but with Northwest Airlines, Inc. (NW)?
(h) Obtain heteroskedatic-robust t-tests for the regression. Why does it not makes sense to use the standard errors (and the t-tests) provided by default with lm()? When would we even consider to use the standard errors provided by lm()?
(I) Test the joint hypothesis that Anna and Rob have the same aver- age travel time given the explanatory variables. To get maximum score on this question you need to first put up the null and the alternative hypotheses and then perform the test and interpret the result.
(j) Does the predicted travel time (statistically) significantly differ between Rob's trip and the same trip but now with Southwest Airlines Co. (WN)? Explain shortly how you determine this.

Regression and Big Data

3. Continue to work with the Airline data but now the complete data set for 2008.
(a) Obtain the sample size of this data.
(b) Run a regression with the following formula: ArrDelay" Origin + Month + Distance using a function presented during the course for handling big data.
(c) What sign does the estimated coefficient on December have? Does it makes sense? Motivate shortly.
(d) What is the predicted delay for Sue who is going to travel 1000 miles, the day before the Swedish "Christmas eve' from Newark Airport (EWR)? Given the results from the regression in 3b.
(e) With the pred_airports function, you can find in the script Predict.airports.exam.R you can obtain the predicted values for each airport and month holding the distance fixed at the sample average. Try to obtain the predicted value for each airport and month.
(f) According to the estimates you have obtain from the regression in 3b, which two months have the lowest respectively the highest predicted delays? Use the predicted values and make two separate plots for these two months. Plot the delays for the 3% largest airports, defined as the airports with most flights during 2008. Make the plots as nice as possible.

Re-sampling methods 1. Simulations. (a) Simulate an experiment...