A simplified (and some may argue, simplistic) introduction to econometrics with linear regression. No formulas inside!

1. What is econometrics? Simple, non-technical introduction on Linear Regression/OLS as a technique

5. What is econometrics?

6. “Econometrics? Isn’t that difficult?”

7. It’s full of formulas… and it could be complex

8. But…

10. This is an attempt to present econometrics as simple as possible…

11. What’s required to learn a little bit of econometrics

12. … lots of curiosity

13. … a little bit of patience

14. … a little bit of brains

15. … confidence in dealing with numbers

16. … a belief that numbers can tell stories

17. Let’s start with a little bit of definition What is econometrics?

27. If we plotted the data, we would indeed see an upward trend… Time t, in months Product users ‘000 In the 1 st month, we see that there are about 5’000 product users By the 30 th month, the number of users have increased to about 40’000 users

29. To answer this question… … we need to understand first the past relationship between the two variables – time and numbers of users . We will then use this understanding of the past to predict what’s going to happen in the next 12 months The Past The Future

30. What bridges the gap between the past and the future… Once we have identified the equation or the model, we will have a better grasp of (1) the past trends and (2) the potentials of the future Linear regression comes into the picture by bridging that gap between the past and the future The Past The Future Linear regression equation

31. With that in mind, let’s look at the chart again

32. From mere observation, we see an uptrend in users across time… Time t, in months Product users ‘000

33. How do we quantify* that uptrend? Time t, in months Product users ‘000 * Remember: In order to project into the future, we need to create a model that quantifies the relationship between time and number of users

34. There are an infinite number of lines that we could use to characterize the uptrend… Time t, in months Product users ‘000 Different people have different views – even when viewing the same set of data: I can argue that the best line is the grey line, another can argue that the blue line is best, and still another can argue that the best line is the pink line

35. Linear regression insists that there is one (and only one) line that would best characterize the trend and the relationship between the two variables

38. Let’s go back a few charts… What OLS does is it objectively goes through these infinite number of lines – and finds the best-fitting line such that the distance between the line and the original data-points are at a minimum OLS does this iteratively – that is, through trial-and-error – until it arrives at the values of m, b, and u that define a line with minimum distance between it and the original data. (Think of OLS as a search-algorithm that tries different m-b-u combinations to achieve the best-fitting line.) Remember: Given any data set, there are an infinite number of lines that can be used to describe the trend. One can choose the “pink” to be the best and rationalize it; another person can argue that the yellow line is the best, and still another third person can defend the blue line. We can argue indefinitely about the merits of each of these infinite number of lines.

39. Going back to the data – the best fitting regression line, after applying OLS is… Time t, in months Product users ‘000

44. Let’s eyeball the model: There seem to be no data-points that are significantly away from the line… Time t, in months Product users ‘000

45. Eyeballing the data, however, brings back subjective interpretations Time t, in months Product users ‘000 One can argue that point at month 11 is significantly away from the line – and so is data for month 24… We therefore need a more accurate, more objective measurement of “fit”

50. Let’s go back to the original question:

53. Let’s now project what’s going to happen in the next 12 months… Time t, in months Product users ‘000 At the end of the next 12 months [by month 42], we can expect to have 543’000 users – if all things remain equal

54. Since we don’t really know what’s going to happen in the future – and we don’t have a perfect model… We can report ranges instead of just a line… The dashed lines indicate the range of expectations for the next 12 months We can expect that there will be about 470’000 to 616’000 users by month 42

55. Are you still there?

56. Take a sigh of relief…