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STATS 330 Assignment2 Write your assignment using R Markdown

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STATS 330 Assignment2 Write your assignment using R Markdown.Knit your report to either a HTML or PDF document.

Create a section for each question. Include all relevant code and output in the final document.

Please keep your code tidy and your plots neat and professional. For example, it’s very useful for the reader if you use informative, readable axis labels rather than allowing the default behaviour of printing the R object

name.

Please refer to the plots in-text when interpreting.

5 presentation marks are available.

Please remember to upload your HTML or PDF document to Canvas by the due date.

Please remember to upload your R Markdown file to Canvas before the deadline, too. If the markers identify an error in your work, being able to run the code you have written can help determine what you did wrong.

Due on 13th April 2022 at 11:00 AM (NZ time)

Question 1

In this exercise, we will explore whether a person’s frequency of prayer describes whether they believe divorce should be more difficult to obtain than it is now. The data set divorce contains information about divlaw : Should divorce in this country be easier or more difficult to obtain than it is now? (See

Table 1) pray : How often does respondent pray? (See Table 2) age : Age of respondent

relig : What is your religious preference? (See Table 3)

1. You will need to do data preparation first before you start building models. 5 marks

a. Recode divlaw into a binary variable that suits the purpose of this study. (See Table

4)

b. Recode pray into the following categories. (See Table 5)

c. Recode relig into the following categories. (See Table 6)

d. Do you think it is reasonable to consider IAP and DK as NA for divlaw ?

2. Make appropriate plots of the response variable with age , pray and relig and comment on what you can observe. 12 marks

3. Fit a logistic regression model with all the predictors ( age , pray and relig ) as main

effects. 2 marks

4. Report the residual deviance and associated degrees of freedom. Can we use this information to determine the goodness of fit of the fitted model? Explain. 4 marks

5. Plot the deviance residuals against the fitted values on the logit scale. What can be concluded from this plot? 2 marks

6. Provide an appropriate residual plot to determine the adequacy of the fitted model and comment on what you can observe. 3 marks

7. Provide a Chi-squared test for each variable included in the model and comment on the results. 3 marks

8. Provide an interpretation of the significant coefficients. 5 marks

9. Which subset of people are predicted to have the highest probability of supporting stricter

divorce laws, and which subset of people are predicted to have the lowest probability of

supporting stricter divorce laws? 4 marks

40 marks

Question 2

The dataset airbnb contains information about 1561 Airbnb listings in Chicago, collected in

2016. The variables in the dataset are: price : the nightly price of the listing (in USD)

rating : the listing’s average rating, on a scale from 1 to 5 room_type : the type of listing (a shared room, an entire house/apartment, a private room) bedrooms : the number of bedrooms the listings has

min_stay : the minimum number of nights to stay in the listing

district : the district in which the listing is located

transit_score : the neighborhood’s rating for access to public transit (0–100)

In this exercise, we are interested in building a model to describe the variation in price using

rating , room_type , bedrooms , min_stay , transit_score and district .

1. Plot the response variable and comment on what you can observe. Describe how we can use

this response variable to fit a linear model. 5 marks

2. Fit a linear model to predict the price using the given predictor variables. 2 marks

3. How well does this model fit the data in terms of . Plot the residuals against the fitted

values and comment on what you can observe. 4 marks

4. Based on the type of the response variable, what distribution is appropriate to use for the

response variable. 3 marks

5. Write down the full model you would fit for the response and predictor variables based on

part 4. 2 marks

6. Fit the model specified in part 5 by using the data given. 2 marks

7. Perform and interpret a test of goodness-of-fit for the model fitted in part 6. 4 marks

8. Produce and comment on appropriate residual plots for the model fitted in part 5. 5 marks

9. Suggest two possible models that you can use to address the problems noted in part 8. 2

marks

10. Fit the models you have suggested in part 9. 3 marks

11. Produce and comment on appropriate residual plots for the models fitted in part 10. 4 marks

12. Do you observe any usual observation(s) in the residual plots obtained in part 11?

Investigate any possible reason(s) for the presence of such observation(s) and comment. 3

marks

13. Compare and comment on the coefficients for the two models you fitted above with the one

you fitted in part 2. Plot fitted values from these three models against the actual

observations and comment on what you can observe. 7 marks

14. Out of these three models, which model would you recommend? Give reasons for your

selection. 4 marks

50 marks

Presentation 5 marks

Total: 95 marks

Appendix

Table 1: Levels used in divlaw

Response Meaning

1 Easier

2 More difficult

3 Stay same

0 IAP, question is inapplicable to this person for some reason

8 DK, don't know

9 NA, question not asked to this individual

 

 

Table 2: Levels used in pray

Response Meaning

1 Several times a day

2 Once a day

3 Several times a week

4 Once a week

5 Less than once a week

6 Never

0 IAP, question is inapplicable to this person for some reason

8 DK, don't know

9 NA, question not asked to this individual

 

 

Table 3: Levels used in relig

Response Meaning

1 Protestant

2 Catholic

3 Jewish

4 None

5 Other

6 Buddhism

7 Hinduism

8 Other eastern religions

9 Muslim/islam

10 Orthodox-christian

11 Christian

12 Native american

13 Inter-nondenominational

98 Don't know

99 NA, question not asked to this individual

 

 

Table 4: Recoded levels in

divlaw

Old code New code

Easier No

More difficult Yes

Stay same No

IAP/DK/NA NA

 

 

Table 5: Recoded levels in pray

Old code New code

Once a day Daily

Several times a day > Daily

Less than once a week < Weekly

Once a week Weekly

Several times a week > Weekly

Never Never

IAP/DK/NA NA

 

 

Table 6: Recoded levels in relig

Old code New code

Protestant Christian

Orthodox-christian Christian

Christian Christian

Inter-nondenominational Christian

Catholic Catholic

Jewish Jewish

Buddhism Eastern

Hinduism Eastern

Other eastern region Eastern

Muslim/islam Muslim

Native american Native american

Other Other

None None

DK/NA NA

Code

R

2