Single variable linear regression: Calculating baseline prediction, SSE, SST, R2 & RMSE:



This post is focused on basic concepts in linear regression and I will share how to calculate baseline prediction, SSE, SST, R2 and RMSE for a single variable linear regression.


The following figure shows three data points and the best-fit regression line: y = 3x + 2.

The x-coordinate, or “x”, is our independent variable and the y-coordinate, or “y”, is our dependent variable.

Baseline Prediction:

Baseline prediction is just the average of values of dependent variables. So in this case:

(2 + 2 + 8) / 3 = 4

It won’t take into account the independent variables and just predict the same outcome. We’ll see in a minute why baseline prediction is important.

Here’s what the baseline model would look like:

regression baseline model


SSE stands for Sum of Squared errors.

Error is the difference between actual and predicted values.

So SSE in this case:

= (2 – 2)^2 + (2 – 5)^2 + (8 – 5)^2

= 0 + 9 + 9

= 18


SST stands for Total Sum of Squares.

Step 1 is to take the difference between Actual values and Baseline values of the dependent variables.

Step 2 is to Square them each and add them up.

So in this case:

= (2 – 4)^2 + (2 – 4)^2 + (8 – 4)^2

= 24


Now R2 is 1 – (SSE/SST)

So in this case:

= 1 – (18/24)

= 0.25


RMSE is Root mean squared error. It can be computed using:

Square Root of (SSE/N) where N is the # of dependent variables.

So in this case, it’s:

SQRT (18/3) = 2.44


Data analytics vs. Data science vs. Business intelligence: what are the key differences/distinctions?


They are used interchangeably since all of them involve working with data to find actionable insights. But I like to differentiate them based on the type of the question you’re asking:

  • What:

What are my sales number for this quarter?

What is the profit for this year to date?

What are my sales number over the past 6 months?

What did the sales look like same quarter last year?

All of these questions are used to report on facts and tools that help you build data models and reports can be classified as “Business Intelligence” tools.

  • Why:

Why is my sales number higher for this quarter compared to last quarter?

Why are we seeing increase in sales over the past 6 months?

Why are we seeing decrease in profit over the past 6 months?

Why does the profit this quarter less compared to same quarter last year?

All of these questions try to figure why something happened? A data analyst typically takes a stab at this. He might use existing Business Intelligence platform to pull data and/or also merge other data sets. He/she then applies data analysis techniques on the data to answer the “why” question and help business user get to the actionable insight.

  • What’s next:

What will be my sales forecast for next year?

What will be our profit next year for Scenario A, B & C?

Which customers will cancel/churn next quarter?

Which new customers will convert to a high-value customer?

All of these questions try to “predict” what will happen next (based on historical data/patterns). Sometimes, you don’t know the questions in the first place so there’s a lot of pro-active thinking going on and usually a “data scientist” are doing that. Sometimes you start with a high level business problem and form “hypothesis” to drive your analysis. All of these can be classified under “data science”.

Now, as you can see as we progressed from What -> Why -> What’s next, the level of sophistication needed to do the analysis also increased. So you need a combination of people, process and technology platform in an organization to go from having a Business Intelligence maturity all the way to achieving data science capabilities.

Here’s a related blog post that I wrote on this a while back: Business Analytics Continuum: – Insight Extractor – Blog

Data Science

..And you can check out other stuff I write about here: Insight Extractor – Blog – Paras Doshi’s Blog on Analytics, Data Science & Business Intelligence.


Looker vs Tableau: How would you compare them in terms of price & capabilities?


Someone asked this on quora so here’s my response: This is a great question — one that I figured it out when I led Analytics at Kiva[.]Org last year so I am happy to add my perspective here on Looker vs Tableau:

Looker vs Tableau

Let’s talk about capabilities first and then price.

Capabilities — Looker vs Tableau

Even though both of these tools are classified under Business Intelligence, they have some pretty clear product differentiation so in this section, I will share that. I will share the three main components of Business Intelligence platforms and then map it back to core strengths of each product.

Business Intelligence platforms typically has three main components:

  1. Data Collection, Storage & Access
  2. Data Modeling
  3. Data Visualization

#1) Data Collection, Storage & Access: Both of these tools don’t do data collection & storage. You will need infrastructure to collect data and store it — typically it is stored in databases. And you can access data from databases using SQL. You will need to connect to these data sources from either of these tools and access data — Note that: On the surface, it might look like Tableau supports more data sources than Looker but there might be workaround to get your data into one of the data sources supported by Looker and take it from there and so I am not awarding extra points to Tableau for this. Also, I am personally a big proponent of using Analytic databases like redshift, vertica, bigquery & Azure DW for Analytics applications which Looker & Tableau both support so calling it a tie here!

#2) Data Modeling: This is Looker’s core strength by a wide margin! Why? This is because of their LookML which is their data modeling layer and I am super impressed by this after using it for a while now! So let’s chat about what data modeling layer means and why you should care.

Data modeling (in this context) means creating data models that take your raw data as input and then it’s cleaned, combined, curated & converted and made ready for data analysis.

Why is this important? Not everyone can clean, curate, combine & convert raw data into analysis-friendly data assets. That’s what data analysts are trained and specialize in. May in the future we will have tools that do that OR maybe we will see plug-and-play (aka turnkey) solutions for few key analysis needs but for now, you need data analysts that can create these data models.

Now there are two ways to create data models:

You can create them on-the-fly (ad-hoc) OR you can publish all of these data models on a platform (like Looker).

There are all sorts of issues with doing it on-the-fly — it works for small teams (<20–30 people) but more than that you need to have some process in place. For instance: You can’t automate data models that you need often so that’s wasted time, Also, you can’t share these models easily with others, creates a single point of failure and if the analyst person is sick or on vacation then no-one gets “insights” from data — the world stops spinning. Yada Yada Yada…So self-service is good after you have few business users who want to consume data.

So what does a self-service platform bring to the table? They help data analyst build these wonderful data-analysis friendly models and publish them so everyone who cares in an org can access it. So the consumer can focus on analysis part and not worry about doing the not-so-good part of making it ready for analysis. Also, this ensures all sorts of other benefits: standardized metric definitions, trusted data sources, better collaboration among analysts, speedier model-delivery process, get out of excel hell and what not!

Think of this way: If you have all key data model available on your self-service platform then your data analyst can focus on 1) advance stuff = more $$$ 2) building more data models (and so eventually they can do more advanced stuff later and more $$$!)

Looker vs Tableau

This is where Looker fits in. Looker is great at this data modeling thing — it’s platform is amazing for anyone looking to solve this problem. You can also do data visualization on top and build dashboards.

Alright, moving on:

#3) Data Visualization: This is Tableau’s forte! No one does data viz better than Tableau, at least right now. There are vendors that are investing significant resources on this and they are close but still Tableau is a leader in this space.

Having said that, let’s map it back to how it help business users & analysts:

Business users and self-service environments:

Tableau is not great at data modeling thing. Yes, you can do basic clean, combine, curate & convert thingy but it doesn’t work well with intermediate to advanced needs. So if you have a self-service data modeling layer already in place that Tableau can connect to and you are looking for a data visualization layer then go for Tableau! You would be able to create some amazing visuals, dashboards and stories that will WOW your business users! But to make sure this scales you need to seriously think about 1) how to overcome the limitations in tableau’s data modeling layer OR 2) use some other tool to build this data modeling layer and connect Tableau to it.

Pro Tip: I highly recommend trying out trials of these products and seeing what works best!


Tableau shines at data discovery! While this certainly helps business users, it’s best leveraged by analyst because whenever they are working on ad-hoc data analysis (one-time, strategic in nature) projects they can be much more effective and discover the underlying trends and patterns in their data by visualizing it using Tableau.

So with that context you might be wondering, What tool did I champion & Implement at Kiva?

This is public knowledge that Kiva is a Looker customer because it’s Logo is on their website so I can share this.

After evaluating about 30+ tools (including Tableau), I ended up championing and eventually leading the initial implementation sprints to implement Looker at Kiva because the goals & vision that we had for Kiva’s data & analytics platform aligned better with having the data modeling layer that met Kiva’s needs. So you need to figure out your goals and vision and then choose the tools with that framework.

Pro Tip #1: It’s insanely hard to figure out what your goals and vision for analytics in an org. To figure this out, you might want to chat with organizations in the same industry at the same size & stage and see what they use. Ask them about what they use and whether it worked for them. Ask them about their Return on investment. This is a great way to get external feedback but you still need to figure out internal needs and prioritize them.

Pro Tip #2: Both of these tools have amazing reviews! You will see them highly ranked in analyst reports too — this is great but it’s important that ever before to clearly define what your organization needs and then map it back to the core strengths of these products (or any other tool for that matter) and go from there!

[I am happy to help evaluate the right tool for you needs, feel free to contact me: Let’s Connect! – Insight Extractor – Blog ]

Pricing — Looker vs Tableau

I can’t talk about Looker’s pricing because it’s not public, I apologize! You need to contact them to get the quote.

However, you can anchor that with Tableau’s pricing which is public: Buy Tableau | Tableau Webstore

Your analyst and power users will need Tableau Desktop/Professional which is $1K and $2K respectively (one-time thing) and then depending on your deployment model: cloud or self-hosted — the price varies:

Looker Tableau Pricing

*Note that Tableau online is a subscription model so you can definitely start small. Let’s say 5 business users in a department and take it from there. If you grow then you can later look at other tools like Looker. (If you are rapidly growing, account for the non-trivial time needed to migrate from one platform to another and so it might be worth it to pick the right tool from the get-go)

Pro Tip: I will encourage you to think about building a ROI model too. You know use some analytics for your analytics projects 😉 — I apologize, couldn’t resist! Anyhow, the point is that instead of just thinking about the “cost”, think about the value-add and anchor your investment figure to that. There’s a reason some analytics tool are priced at let’s say $1000 vs some tools priced at $100,000 — both of them have different value proposition and if you know how to extract value of the tool and can project it then you can get better ROI!

Hope that helps! If I can be of any further help, email me or comment here! Let’s Connect! – Insight Extractor – Blog


Cheat Sheet to Pick the right graph or chart for your data:


I have two resources that I use sometimes to pick the right graph or chart for data visualization.

#1: Chart Suggestions:

chart data

#2: Online Tool

(By Juice Labs)

chart pick choose online tool

Introduction to SQL Performance Tuning for Data Analysts



SQL is a common language used by data analysts (and even business users!) for data analysis — one of the reasons is popular is because it’s not that hard to pick it up. Sure, there is some learning curve especially if you don’t have a computer programming background but once you learn some basic commands, you will be able to apply it and answer a lot of questions. So it does give you lot of power! But sometimes you run into issues where your SQL queries are taking forever to complete and you wonder why that’s the case. In this post, I am going to introduce you to performance tuning that will help to troubleshoot next time you run into performance problems.

Performance Tuning SQL

Performance Tuning SQL

Performance tuning Hierarchy

your queries are slow due to one of the three reasons listed below:

#1: SQL Query optimization

#2: Database software, environment & optimization

#3. Hardware

You should start at Level 1 which is query optimization and then work your way down to other levels. This post will focus on SQL Query optimization as that is something you can control and it is also the most common root cause. Let’s focus on this first and then we will explore other options.

Performance Tuning SQL Queries

Depending on your skill level, you can look at a lot of things. But for the purpose of this blog post lets say you have beginner – intermediate SQL Knowledge and with that, you can look at following things:

  1. Size of your tables: If you are querying tables with millions of rows then that is going to slow down your queries. You can start off with limiting the amount of rows that you are working with using SQL clauses like LIMIT/TOP (depends on database system you are using) that will reduce the number of rows that database works with. This is great for exploratory analysis where you don’t need to look at all rows. Also, you should consider using “where” clause when it’s applicable. So let’s say you just care about a particular product category OR a particular product category then put where clauses where it’s applicable.
  2. Complex joins & aggregations: If you trying to join tables in such a way that returns a large number of rows then it’s going to be slow! If possible you can apply step 1 (limit your rows) to this as well — so let’s say you have two tables that are trying to join but you don’t need everything from table 1 then consider putting where clause on table 1. That would help. Also, if you are using aggregations along with joining tables then you could consider doing aggregations on individual tables first and put them in a subquery and then use them to join with other tables. Here’s an example where you are aggregating the table before joining them with other tables:

    SELECT cat.product_category,
    FROM (
    SELECT p.product_name,
    COUNT(*) AS products
    FROM Product p
    GROUP BY 1
    ) sub
    JOIN ProductCategory cat
    ON cat.product_name = sub.product_name

  3. Query plan: Also, how do you know which statement is a bottleneck in your queries. You could consider running them individually and see but even if that doesn’t help then you can use something called a “Query plan” — depending on the database system you are using the commands can differ but you can try searching the help section for that. It’s called Query/Execution plans and they help you see the order in which the query will be executed. Also, it will have “estimated” time to run stats (which may or may not be accurate) but still good starting point to see how long it might take for complex queries especially as you make changes, you can continuously evaluate without having to run the query. There’s a bit of learning curve on how to read execution/query plans but they are a great way to check the bottlenecks in a query that you wrote. You can try using a command like “EXPLAIN” before your query and check your database help section to see if that’s not the command.

Database software, Environment, Optimization & Hardware:

Let’s say you have tried everything you could to tune your SQL queries then it’s move to explore other options:

#2: Database software, environment & optimization: This is usually owned by Dev Ops or IT team and you will have to work with them. Depending on your team size, there might be a DBA, System Admin or DevOps engineer responsible for this. Here’s few things you should check out along with the IT team:

  • Are there a lot of users running queries at the same time?
  • Upgrade to database software and/or perform database optimization (e.g. indexing)
  • Consider evaluating a database that supports analytics better like Vertica, Redshift, Teradata, Google BigQuery, Microsft Azure SQL Data Warehouse among others — if you have 20+ users hitting a database for querying and have tables with 25M+ rows then this is worth evaluating! Your mileage may vary (depending on your hardware) but I am sharing these thresholds just so you have a starting point. These databases are different in architecture compared to something like MySQL which will bog down as you start to scale analytics in your org.
  • Are you querying a production database that also used to support other apps? If so, consider requesting a copy of a database to work with. IT should be able to set up a copy that gets refreshed let’s say nightly and that should help. You should then route all SQL users to this database and restrict access to production database.

#3: Hardware:

Since database is a software, it is constrained by the resources that it is allocated at hardware level just like any other software. You should dive deeper into this if #1 & #2 don’t work out — This is not the most common root-cause but as a rule of thumb, you should be scaling your hardware resources as other systems are scaled too. if that’s not done regularly then you will hit hardware issues. Also, don’t just upgrade your hardware, as I referred to earlier in #2, consider looking into databases that are better for analytics like vertica, redshift, bigquery etc. Compare all options & do an ROI analysis as upgrading hardware is usually a “duct-tape” solution and you will run into it again if you continue to grow.


So you now have a framework which should help you when you run into SQL performance problems! Now it’s your turn, I would love to hear about what you did when you ran into performance problems in any of your data analysis project.

Introduction to Goal Seek & Solver capabilities in Excel:


What-if Analysis is a pretty common analysis done by decision makers. Often, they would just create simple excel tables and adjust their variables manually until they get an answer that works. But instead of doing it manually there are features available in excel that will make your life much easier and analysis much more accurate. So, the goal of this blog post is to introduce you to the Goal Seek and Solver feature to help you do what-if analysis in Excel.

#1. Goal Seek:

Let’s say you are a CEO of an e-commerce startup and wondering about what factors you need to focus on to increase revenue. Here’s what the data (*assume per month) looks like when you start out:

excel-goal-seek-1And you want to increase the Revenue to $150K from $125K. The three levers you can pull are website visitors, conversion and revenue per customer.

Now you could manually tweak the values for this variables till you get to $150K but as I promised earlier, there’s a better way!

Let’s start with Goal Seek.

You need to set two variables for Goal Seek.

a. Your goal — which in this case is 150K

b. The variable that needs to be changed to achieve that goal — note that you can specify just one variable to do so. So you need to choose out of the three above what you would like to focus on. Let’s say you want to focus on conversion rate.

So once you have these two things — from the Data Tab in Excel, Go To What-if Analysis, Goal Seek:

excel-goal-seek-2Now, specify the values. For this example, we want to figure out what should be the new conversion rate so that our revenue will be $150K. So here’s an example of how that would look on Goal-seek:

excel-goal-seek-3After entering the values, you will see the status — you can click “OK” to keep the solution and cancel to go back to what you had:

excel-goal-seek-4Perfect! So you need to increase the conversion rate from 1.25% to 1.5% to get to the goal that you had set!

#2: Solver add-in

So, you worked on improving the conversion rate for next month or two and you & your team found out that it’s getting really hard to increase it above 1.35% — And also you found that with the less effort you can move the needle on other variables (website visitors & revenue per customer). Now Goal Seek allows you just set one variable so if you more variables than it doesn’t serve the purpose that well! That is where Solver add-in helps.

Think of Solver as advanced Goal seek where you can set more than one cell that can change. You can also set constraints on what the values could be for all the variables that can change.

Now, for our scenario, the conversion rate is at 1.35% but you want to see the possible changes that you can make for website visitors and revenue per customer to reach $150K.

You also know that you can’t above 1,100,000 Website visitors per month and also need to have less than $11 as revenue per customer.

You will need to enable the Solver add-in in Excel and once you do that you will see that in the Data Tab.

Once you have it, open it and fill up the information needed in the dialog box:

a,. Set objective to Total Revenue with value of 150000

b. By changing cells to: Website Visitors and Revenue per Customer

c. Constraints. Website Visitors <= 1,100,000 and Revenue Per Customer < $11

solver-excel-1After that click on Solve.

if it found a solution, it would show you that on Excel and also give you additional options to whether you want to keep the solver solution or restore it to original values:

For our scenario, it suggesting that with website visitors to 1,010,101 and revenue per customer to $11, we should hit our goal.

solver-excel-2Click on OK when you’re done.


In this post, we saw how you can use Goal Seek and Solver add-in using an e-commerce scenario but you these techniques can be applied to wide variety of data analysis problems that can be solved using “what-if” techniques.

Hope this was helpful and I would love to hear from you about how will you use this in your work? Or if you use it already then what do you use it for?

As a data analyst for the CEO in an e-commerce company, what kind of reports are expected of me?


Someone asked this on Quora and here’s my reply:

As a data analyst, you should work with the CEO (or other decision makers) on a quarterly (or more frequent if possible) and learn about #1 Strategic objectives and initiatives — #2 after that, you should work together and figure out how analytics could help these initiatives.

So why is learning about strategic initiatives from the executives important?

  1. Because analytics could be applied to lot of problems but you and your team might just have limited bandwidth.
  2. Also, executives want to stay focused on what’s important now and so if your priorities align then you are much likely to succeed in the role.

Let’s take an example:

Scenario 1: As a data analyst, you create bunch of reports from let’s say Google Analytics and throw them at the CEO! It has everything like visitor stats, acquisition stats, retention stats, behavior stats, conversion stats among others! Now by doing so, executives might get what they asked for but then they will still have to go through the reports and map it back to their strategic initiatives and figure out the recommendations on their own. Also, executives might not have the time to do this and may miss critical insights.

Scenario 2: You know that the one of the strategic initiate for the quarter is to improve the conversion rate from landing pages to order-complete page from 1.25% to 1.40% — so your analysis that you send to the executive would not only be focused on just that but also include “recommendations” — like it seems that there is a significant drop-off after customers learn about shipping cost. Then the executive could use those recommendations to drive actions. There’s also another benefit: Any ad-hoc data request that doesn’t align with the strategic objectives can be postponed (or de-prioritized) and let’s you focus on what’s most important for the company.

I prefer scenario #2. And try to create this culture wherever I am working. Executives should be open to sharing strategic initiatives at high-level with everyone in the company and help align everyone’s priorities.

Note: This doesn’t mean that you don’t create reports, you still do that for broader consumption — especially the Key Performance indicators that are key for success but you should look at automating most of that and focus on data analysis and find recommendations that the executives could take some action on.