Write a Rmarkdown code file (gv900-HW2.Rmd) to complete the following tasks.
RULES
Submit three files, and three files only. That is, submit (1) the coversheet ( ESSAY COVERSHEET 2020-2021.docx, available on Moodle) and (2) your Rmarkdown code script (gv900-HW2-yourID.Rmd). (3) the html document showing your code, your comments, results, and graphics (gv900-HW2-yourID.html). (minus 5 points if fail to do so)
Make sure that you delete your name from your Rmd code script and html document.
(minus 5 points if fail to do so)
• Execute everything before you submit (e.g., CTRL +A & CTRL + Return on a Windows PC; Command +A & Command +Enter on a Mac), and make sure your file runs without an error. (minus 5 points if fail to do so)
• Your Html output must have a proper header. (minus 5 points if fail to do so)
In your Rmd file, add comments and annotations to everything you do. Try to make your code file look like my code file. Don’t copy and paste all the questions into your Rmd code file, but do show me the question number for each question. (minus 5 points if fail to do so)
TASKS
1. You are going to use the following 6 R packages: ggplot2, gmodels, Hmisc, stargazer, effects, and gridExtra. Load all the packages. [2 points]
2. Load Titanic passenger survival dataset available on Moodle (titanic.csv), and store it as an object named td. [2 points]
3. The unit of observation is individual passengers. How many passengers does the dataset have? That is, how many rows are there in the dataset? Provide a command to get the answer. Also, write your answer in a comment line. [2 points]
4. The dataset contains various information on passengers, including their name (name) and whether or not they survived (survived). The dummy variable survived is coded as 1 if a passenger survived and 0 otherwise. Create a simple frequency table of the survived variable (that is, there is no need to change the column names or to obtain relative percentages for this task; one line of command is sufficient) to see how many passengers survived and how many did not make it. Provide a command to create a frequency table of this variable (no need to write a comment). [2 points]
5. Calculate the survival percentage. Provide command(s) to calculate it. Also, write your answer in a comment line. [2 points]
6. The data set contains a variable named pclass, which is coded as 1 (= passenger has a 1st class ticket; for those of you who don’t know, 1st class tickets are more expensive than 2nd class tickets, 2nd class more expensive than 3rd class), 2 (= 2nd class ticket), and 3 (= 3rd class ticket). This ordinal (ordered categorical) variable could be used as a proxy for socio-economic class of passengers. Create a simple frequency table of this variable (that is, there is no need to change the column names; one line of command is sufficient) to see the distribution of this variable. Provide a command to create a frequency table of this variable (no need to write a comment). [2 points]
7. In tasks 7–11, we will analyze the relationship between socio-economic class of passengers and their survival using one of the three bivariate hypothesis testing methods you have learned in Weeks 6 & 7. The question we ask here is: how does socio-economic class of passengers influence the likelihood of passenger survival? Let’s say we hypothesize that socio-economic class of passengers is positively associated with passenger survival. First, what are the dependent and independent variables in our investigation? Provide your answers in a comment line. [2 points]
8. Second, create a two-way frequency table (a.k.a, cross tabulation) of the two variables, pclass and survived. Provide a command to create such a table (no need to write a comment). Make sure that (1) values of the dependent variable are shown in rows and the independent variable in columns, (2) your table shows column percentages but not row percentages, cell percentages, or χ2 contributions, and (3) your table produces a χ2 test statistic. [6 points]
9. Read the table you produced the above and answer a few questions. (a) What is the survival percentage among the 1st class passengers? (b) What is the survival percentage among the 2nd class passengers? (c) What is the survival percentage among the 3rd class passengers? Provide your answers in comment lines. [3 points]
10. Would you say that the relationship between survived and pclass is consistent with our hypothesis I described in task 7? Why or why not? There is no need to comment on statistical significance, but do comment on the pattern observed in the sample. Provide your answers in a comment line. [3 points]
11. Fill in the blanks of the following statements that summarize the results. Provide your answers in a comment line. You only need to write four options, such as (a), (b), (c), etc., in the correct order. [8 points]
Since the test statistic produces a p-value smaller than , we can the null hypothesis of no association at % confidence level. We thus support for our hypothesis.
(a) 173 (b) 172 (c) 128 (d) 127 (e) 99.9 (f) 99
(g) 95 (h) 90 (i) 0.1 (j) 0.05 (k) 0.01 (l) 0.001
(m) accept (n) reject (o) find (p) do not find
12. The dataset contains a variable named fare, which is the price of the ticket each passenger has. It is shown in pre-1970 GBP. (Note: £ 1 in 1911 is equivalent in purchasing power to about £ 112 in 2018.) Do female passengers tend to have a more expensive ticket compared with male passengers? Explore the relationship between the female variable (coded as “Female” for female passengers and “Male” for male passengers) and fare. Choose an appropriate bivariate statistical testing method for these two variables from the three methods you have learned in Weeks 6 & 7, and perform the test. Provide command(s) to perform the analysis. (Hint: I am not asking you to run a regression.) [5 points]
13. Interpret the results of the bivariate test you performed above and answer the question (do female passengers tend to have a more expensive ticket?). Comment on the observed pattern in the sample as well as the statistical significance, and draw a conclusion (i.e., answer the question posed here). Your answers must have up to three sentences. [6 points]
14. The dataset contains a variable named age (age of the passenger). Do older passengers tend to have a more expensive ticket compared with younger passengers? Explore the relationship between age and fare graphically. That is, create a plot that shows the relationship between these two variables using the ggplot function. Provide commands to create the plot. [5 points]
15. Perform an appropriate bivariate statistical test (again, choose one from the three methods covered in Weeks 6 & 7) to explore the relationship between age and fare. Provide command(s) to perform the analysis. (Hint: I am not asking you to run a regression.) [5 points]
16. Interpret the results of the bivariate test you performed above and answer the question (do older passengers tend to have a more expensive ticket?). Comment on the observed pattern in the sample as well as the statistical significance, and draw a conclusion (i.e., answer the question posed here). Your written answers must have up to three sentences. [6 points]
17. Regress fare on age, and produce a regression table using the stargazer function. [4 points]
18. Create a plot that illustrates the estimated effect of age on fare based on the model you estimated above. [3 points]
19. Judging from the numerical and graphical results of the regression analysis, would you say that age and fare are positively related? Comment on the observed pattern in the sample as well as the statistical significance, and draw a conclusion. [6 points]
20. Graphically explore the relationship between age and fare, holding constant the female variable. That is, create a plot using the ggplot function that shows the relationship between age and fare for female and male passengers separately. Try to have one plot that has two panels (one for female and one for male). [5 points]
21. Regress fare on age and female, and produce a regression table using the stargazer
function that summarizes the results of this model and the model you estimated in task
17. [4 points]
22. Which one of the two regression models performs better? Fill in the blanks of the following statement. Provide your answers in a comment line. You only need to write four options, such as (a), (b), (c), etc., in the correct order. [8 points]
Since is for the model, the model fits the data better.
(a) standard error (b) p value (c) R2 (d) Adjusted R2 (e) the number of stars (f) smaller (g) greater (h) first (i) second
23. Create a plot that illustrates the estimated effect of female on fare based on the second regression model you estimated. [3 points]
24. Create a plot that illustrates the estimated effect of age on fare for male and female passengers separately based on the second regression model you estimated. Try to have one plot that has two panels (one for female and one for male). [6 points]
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