# How linear regression can be used - explanation for grandmothers

Educational question.

Suppose you have to explain linear regression to your granny. She is well educated, she knows even the idea of the hypothesis testing, but before you start to tell her what regression is she asks you: "Why do I need to study a regression? How could it help me?"

The problem is to explain the goals and benefits of a linear regression without mathematical terminology (without definition of linearity, for example). Can it be done?

My variant is "Suppose we have Y and X - vectors of equal length (continuous measurements). We want to study if Y has a relationship with X. Linear regression can help us to establish properties of one particular type of a relationship".

• I'm sorry, but I think you should refuse to teach it if you are not already able to answer this question. – Peter Flom May 26 '16 at 11:08
• @PeterFlom I am able, I am not satisfied with my answer. Prediction and "linear" relationships do not sound really intuitive. I am always trying to say why it is useful to study a method before the explanation of the method, but I can not do it with the linear regression. It is easy to explain method first and then goals of the regression, but it is not so easy vice versa. – German Demidov May 26 '16 at 13:09
• @PeterFlom in other words - how to explain simple linear regression to a grandma without using the definition of linear equation $y = ax + b + \epsilon$? – German Demidov May 26 '16 at 13:15
• Maybe you can ask your grandma how she would draw a line that best 'fits' a cloud of points? – user83346 May 26 '16 at 13:54
• Linear regression is basically a fancy way of comparing means, and people understand means. Hence, I would use an explanation involving means. As in, what do people earn on average (a.k.a $y = a + \epsilon$)? But hey, maybe we should take into account different education levels. What do people in different education levels earn (a.k.a $y = a + b*edu + \epsilon$), and so forth... Describing regression in terms of the conditional expectation is quite powerful in my experience. – coffeinjunky May 26 '16 at 13:56

## 3 Answers

I would start with some games: give the person you want to teach many continuous numbers which represent a group of people's weight, and ask him/her to predict next. I would say, the person is very likely to use average of all numbers for the prediction. Ask the person why. Try to plant a seed to say using mean is essentially to have a predictor: $y=\beta_0$

Now, we will go to next game: in addition to only give the person predicting target, i.e., weight, give him/her additional information: height. Apparently height is very useful, in most cases, the taller suggests heavier. But the question is: what is the predictor / formula.

You can give him/her some formula got from the regression, such as $y=\beta_0+\beta_1x$ and let the him/her to use this for prediction. I think him/her will like the idea.

When him/her ask you how did you get the formula, you can tell the whole "linear regression" story, i.e., what the $\beta_0$,$\beta_1$ represent for and how to get them.

• Thank you! That is what I was asking for. It is pretty intuitive. – German Demidov May 26 '16 at 14:13

I have had to do this before. I thought that comparing to a cab ride was easy.

You have a flat fee to get into the cab even if you go nowhere and then you pay a fee per mile.

Now, what if you don't know the fees but have a history of trip prices?

That was easy for people to understand since that's something that they deal with often here where I live.

Linear regression fits a line to data: Linear regression as estimating a conditional expectation function:

• This is immediately useful for simple forecasting. Tell me x, and I can say something about y.
• For example, forecast plant growth based upon sunlight exposure.

Linear regression as estimating causal effects:

• In some situations (eg. when variation in x is exogenously introduced by the researcher), linear regression can estimate causal effects.
• If sunlight exposure is randomly assigned by researchers, the regression line would estimate the causal effect of sun exposure on plant growth (i.e. the local average treatment effect).

Linear, ordinary least squares regression is the starting place for all sorts of more advanced estimation techniques. Linear regression is to data analysis as salt is to cooking. You don't have to add it, but it's everywhere.

• good point! I will use it for sure, it is short and meaningful. But I need to explain linear regression for the granny who is doing research, and I need to explain how it can be used in the research. Fitting line tells nothing about possible benefits of using this particular method for the research... – German Demidov May 26 '16 at 21:30
• Maybe linear regression would be anti-beneficial to granny's research. Maybe granny would benefit more from nonlinear regression? Maybe granny would benefit from constraints on parameters? From non-identity error covariance matrix, etc. or do you already know granny's research problem, and are confident linear regression will be beneficial to her? Or is it only a gateway drug to more sophisticated methods? – Mark L. Stone May 26 '16 at 21:43
• @GermanDemidov Hmm. Explaining when fitting a regression line is straight forecasting vs. when fitting a regression line estimates some causal effect may get tricky. – Matthew Gunn May 26 '16 at 21:45
• @MarkL.Stone I am a bit confused with your proposition. I want to explain correctly how and when a granny should use a linear regression. How can it be anti-beneficial? She will be able to solve problems that can be solved with the linear regression (if i will do my job well). It is not possible to learn all the methods. A granny can be a medical doctor - she does not have time for learning sophisticated methods, she is busy with her medical stuff. – German Demidov May 26 '16 at 21:59
• @MatthewGunn I did not think about it. We fit the same model, but does good forecasting leads to existing of causal effects? Seems that yes... – German Demidov May 26 '16 at 22:02