Do these visuals convey information about the property tax rates?

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Instructions

This PDF contains a long form version of the questions in HackerRank in addition to a data appendix which is required to answer a few of the questions. Please refer to the HackerRank test to submit your answers. As you answer the questions in HackerRank, please keep a copy of your answers for your own reference. This will help you to discuss your answers during the technical interview. Responses should be your own; plagiarism will not be accepted.

Visualizing Data

This section assesses the ability to interpret and communicate insights. The Boston Housing data, which is summarized in the appendix, was used to make the visuals in this section.

Question 1

Business leaders would like to understand the relationship between Charles River proximity and property tax rates, defined as the percent of tax paid in relation to home value. An analyst prepared the four visuals below.

a) Do these visuals convey information about the property tax rates? If not, what changes would you make? (Remember to refer to the appendix for data details)

b) Which of the chart types would you recommend including in the report and why?

Question 2

What cosmetic changes would you make to the visual you chose in the previous question to increase visual appeal and interpretability? In your report to business leaders, how would you describe the plot in one sentence?

 Modeling  Data

This section assesses the ability to think critically about variables and how they can be used to predict a desired outcome. Core competencies include understanding distributions in data, making appropriate data transformations, and selecting an appropriate model. The Boston Housing Data Exploration in the Appendix should be used for this section.

Question 3:

Predicting Tax:

a) A linear regression model to predict tax was fit using medv, rad, age and zn. Based on the data summary in the appendix, what additional feature transformations or feature engineering would you consider to better prepare the data for a linear regression model? Consider only the tax, rad, age and zn variables.

b) A co-worker is thinking about adding cmedv as and additional regressor to the model? Do you think this a good idea? Support your answer.

Question 4

Predicting River Proximity: Using the Boston Housing data, you want to predict which tracts are adjacent to the Charles River (as denoted by the chas variable). Propose an interpretable model to investigate the relationship between the covariates (x variables) and chas variable (y variable or target). Explain how you would use the model and its output to provide evidence of the strength and confidence in the relationship.

Question 5

A realtor thinks that if all other variables are held equal, a tract on the Charles River increases median home values by $6,500. To test the realtor’s hypothesis, you created a linear regression model with chas as a covariate (Note that medv is in $1,000’s of dollars). The coefficient associated with chas was 5.01 with a standard error of 0.84. Is there evidence to reject the realtor’s claim at the 95% confidence level? Additionally, how would you defend this analysis with the realtor (who has no knowledge of linear models)?

 Question 6

Predicting Property Tax Amounts: A local realtor wants to use the Boston Housing data to provide tax estimates for clients. A Data Scientist used the code below to fit a random forest model using the Boston Housing data.

a) What percentage of the data is being used to train the model?

b) After seeing the results the model developer is surprised to see that the error metric for Approach 3 is much higher than Approach 1 and Approach 2. Is the error value for Approach 3 correct, if not, how would you fix the value?

c) A co-worker reviews the code and suggests that the error metrics in the results for Approach 1 and Approach 2 are optimistic (better than they actually are). Why might the co-worker have this belief?

d) Approach 1 and 2 seem to have the same error? Is this result surprising? Support your answer.

Attachments:

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