An Analysis of Salaries and Cost of Living in Different US Cities

By James Brunner and Vyoma Jani

Introduction

As computer science majors, we hear many stories about people working their dream jobs in Silicon Valley. Top companies and high pay definitely seem appealing! But we've also heard that the Bay Area is a very expensive place to live, so is it really worth moving there for the high pay?

This tutorial is going to explore the salaries, total years of experience, and other factors for a number of computer scientists across the country. Then, it will look into the cost of living in each of these locations, before determining what cities are best to live in and which ones may be better to avoid. We'll be going through the entire data science pipeline, from gathering the data and organizing it, to performing exploratory data analysis and machine learning on the data collected!

Data Collection

The first step in our process is to scour the web in search of relevant data. First, we will be looking at salary data from Levels.fyi. This dataset contains information about employees from various companies, levels, roles, locations, and paygrades, all collected from users who voluntarily provided their information.

To read in the dataset, we will first generate an HTTP get request using the requests library, and then we will use pandas, a Python library popular for data manipulation and analysis, to convert the json file from the get request into a dataframe.

We will also be looking at the following dataset from Numbeo.com, which provides information regarding the cost of living for various US cities, breaking down the total index into subdivisions like rent index or groceries index. This information is similarly collected voluntarily from users.

Like before, we will be using pandas and the requests library, but we will also be needing the BeautifulSoup library to parse the html data from the request into the dataframe.

All of the Numbeo indices are relative to New York City, meaning New York City will have 100% for each index. If a city has, for example, index 120 for a given category, the city is on average 20% more expensive for that category than New York City.

The indices that the Numbeo data is organized into signify the following (taken from the Numbeo website):

Note that the information from Numbeo is from 2020, whereas the information from Levels.fyi is from 2017 to 2020. While we will not be analyzing the data over time, the year may have an effect on the other variables in the data.

Data Processing

Now that we have gathered our two datasets, we will tidy up the data to make it easier to analyze. For the Levels.fyi data, we will again be needing pandas, and we're also importing the datetime module to help us convert the timestamp information into datetime objects, which will standardize the time.

For the Levels.fyi dataset, we observe that many of the numeric columns, like totalyearlycompensation, are being stored as strings in the datasets. Because we will be interpreting the values as numbers instead of strings, we will convert the values in those numeric columns to numbers.

Also, because we are computer science majors, we're only focusing on computer science jobs!

Before moving into exploratory data analysis, it is important to check our data for outliers and for any values that may have errors or may have been computed incorrectly.

From these summary statistics, we can observe there are some serious outliers. The mean base salary is $3,287,000, which indicates that we may have some faulty values causing the data to be left-skewed. The same appears to be true for stock grant value and bonus. We can also see how significant the outliers get by observing how large the max for each column is in comparison to the 75th percentile.

These outliers appear to be due to an error of how users input their salary information. The expectation of Level.fyi was that users would input their salary in thousands (e.g. 100 would be a salary of 100,000), however many put their data in without knowing this, leading their salary to be 1,000 times what it actually is!

We want to avoid these outliers to prevent our analysis from being skewed, so we will trim the 2.5% highest and lowest salaries from our dataset. Note that there is a risk of introducing bias here, since it is possible that those trimmed salaries are far from data for a reason relevant to our analysis.

Our next step in data preparation involves filtering out all jobs that are not located in the United States. We can observe that in the location column of the salaries dataset, locations in the United States are formatted as "City, State", while other countries (such as Canada) are formatted as "City, State/Province, Country". Using Regular Expressions, we can easily filter out these rows.

Now that both datasets have been properly cleaned, the last step is to merge them together. One noticeable problem is that the Numbeo dataset does not contain all the same cities as the Levels.fyi dataset, and therefore we cannot make a simple join between the two.

Instead, since major cities have an influence on the economics of nearby towns, we will use an algorithm to join each Levels.fyi entry to a closest neighboring city that is in the Numbeo dataset, as long as they are within a reasonable distance from each other.

We will also discard any rows that cannot match a city in our algorithm, as we consider those jobs too far from major U.S. cities and we are not interested in those for the purpose of this analysis.

For the algorithm, we will make use of the Geopy library, which offers tools to locate coordinates across the globe.

From the output above, we can see we did not lose any major cities.

Data Exploration and Analysis

Now that are datasets are clean and organized together, it is time to analyze them!

We will be using Plotly and Seaborn to construct various plots and figures to examine the dataset. We will also use Folium to render a map visual of the data based on location.

First, we will examine the relationship between years of experience and base salary using a scatterplot. We want to determine whetehr the relationship is linear, so we will plot a line of best fit on top.

plot1.png

It looks like there's a positive linear relationship between years of experience and base salary!

However, does this relationship extend for all job positions? Or are there specific Computer Science roles that have a different relationship between base salary and years of experience?

Below, we plot the years of experience against the base salary of the 7 roles we are looking to study. We will create separate scatterplots for the roles, and will again plot a line of best fit to see if there is some type of linear relationship between the two for each role.

plot2.png

Based on the above plots, we can see a positive correlation between years of experience and base salary for each role. It looks like the base salary increases relatively slowly over years of experience for roles like Software Engineering Manager, compared to roles like Software Engineer.

Now we want to narrow our focus to specific cities. Below, we calculate the average base salary per US city in the dataframe.

First, let's take a look at what locations have the highest paying jobs. We will create a map that displays different colored circles on cities depending on their average salary to see where the higher paying jobs are located.

As we can see from the black circles, the highest paying computer science jobs are on the coasts. However, there are still relatively high paying jobs in non-coastal areas like Pittsburgh or Austin, based on the yellow circles.

We want to take a closer look at the 10 highest paying locations to get a better sense of the relationship between years of experience and base salary there. Once again, we plot a matrix of scatterplots below.

plot4.png

It seems that all the cities have positive linear relationships between years of experience and base salary. However, some cities, like San Francisco, have a larger increase in base salary as experience increases, as can be seen by the steeper slope in those graphs. Meanwhile, Pittsburgh and Irvine increase at slower rates. So far, based on salary alone, it seems like the Bay Area is a great place to live, and it offers high growth opportunities for employees. But is the salary worth the cost?

Now, we turn our attention to the cost of living as it relates to salaries, locations, and other factors. First, we will compare base salary to the cost of living index of each location using another scatterplot.

plot5.png

It's a little hard to tell if the above line of best fit actually represents the data well, since the points are all over the place. Thus, we'll create a matrix of correlations between base salary and the different types of cost of living indices to see if there's any more specific linear relationships.

The above correlation matrix indicates that we have a slight positive relationship between base salary and every Numbeo index. The strongest relationships base salary has appear to be with Rent Index and Cost of Living Plus Rent Index, with correlations of 0.3. We'll focus on just the cost of living plus rent index.

We've seen what the highest paying cities are, and we've seen the positive correlation between cost of living plus rent index and base salaries. Now, we're going to combine these two pieces of information together in a histogram below, which graphs the rent index of the 20 highest paying cities.

plot6.png

This plot highlights certain cities as being relatively expensive to live in compared to cities that pay similarly. San Francisco pays the most, but it is also extremely expensive to live in. Meanwhile, cities like New York, Boston, and Washington DC show peaks in the graph, indicating that they are relatively expensive to live in given their average salaries compared to similar cities. Meanwhile, Pittsburgh and Little Rock, for example, seem much cheaper to live in relative to otehr cities with similar average salaries, as we can see dips in the histogram at those cities.

Regression and Machine Learning

Now that we have analyzed the data, we can begin using the analysis to make predictions about a person's salary based on their role, years of experience, and location. We will be performing a multiple linear regression analysis to predict salary.

Learn more about multiple linear regression here: https://www.jmp.com/en_us/statistics-knowledge-portal/what-is-multiple-regression/mlr-with-interactions.html

Below, we use the Statsmodel library to perform ordinary least squares regression with multiple interaction terms. Our null hypothesis is that there is no relationship between role, experience, location, and salary; we will analyze whether this is the case, or whether we should reject the null hypothesis.

As we can see in the model, most of the p-values are very low, with the exception of a handful of cities. While the null hypothesis may be applicable for those cities, overall, we can reject the null hypothesis of no relationship and use this model to predict salaries!

As an example, we'll look at the base salary for software engineers with 0 years of experience across the country.

Now we have a way to predict what your salary will be at a given level of experience for a given role in a specific location. We now want to figure out what city will give you the best bang for your buck - which one will pay the most while still being cheap to live in.

To do this, we will perform the following simple calculation:

Expected Base Salary ⁄ Cost of Living Index

Where the higher the calculated value, the more cost-effective the location is.

Below, we'll try to figure out what the most cost-effective cities are for software engineers with 0 years of experience.

Now this is interesting! Only one of the top 10 highest paying cities seems to have a very good ratio of base salary to cost of living: Pittsburgh! But it's not even first, the number one best city to live in for software engineers with 0 experience, in terms of salary and cost of living, is Little Rock.

This was just one example how how to use the linear model; try putting other roles or years of experiences in to see what their salary estimates and best cities are!

Conclusion

Based on our analysis and predictions, it seems Silicon Valley is not the best place to live in terms of salary and prices. Even though cities in the Bay Area do pay a lot of money, they are so expensive that it may not be worth moving there. In fact, none of the popular coastal cities in the Top 10 seem to be cost-effective places to live in. The best bang for your buck is smaller cities and towns further from the coasts, as they have a relatively high base salary for low cost of living for various CS roles and years of experience.

One thing to note is, because we narrowed down our data set to salaries from companies that appear many times, our data may be restricted to primarily large-scale private companies, as only they were able to provide sufficient information for analysis. It may be interesting to look deeper into other types of companies to see if the analysis changes.

We would like to give a special shoutout to Dr. John Dickerson at University of Maryland for being an outstanding professor and showing us the unlimited possibilities in the field of data science!

Feel free to build on this tutorial! This is just one example of the data science pipeline, there's so much more to explore and analyze. We plan to use the regression analysis above as a backend for a salary and cost of living calculator, for which we will build a frontend UI for. Be creative!