# Explain regression to 7 years old [closed]

Please give a clean, simple, explanatory answer that any 7 yr old can understand.

You can also link to a regression guide that is very good and simple. Should be fully explanatory all the way through. That's what makes a good, not bad, writing to learn from.

Some sub-questions within my main question are:

• What is the purpose of regression?
• Why do we need it?
• What does it do?
• What specific category of math does it fall under, if any?
• Can you use a calculator on the Web to automatically calculate a regression? what's a good site that has this calculator or software to download and perform this function
• What does the result of a regression tell you? or suppose to tell you?
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You need to focus this question more. At present, it isn't really answerable or a good fit for this site. (You may want to read our FAQ.) For starters, have you read the Wikipedia page? There is a lot of info there, perhaps you should try that & come back with a more focused question. –  gung Sep 7 '12 at 2:53
there's lots of info that nobody understands. the question is not asking for that. and this is focused -- what is a regression????? how is anyone suppose to make it more focused? if nobody answers it and just votes it down, then it's a roadblock to learning so thanks for supporting roadblocks to leraning. gj –  kittensatplay Sep 7 '12 at 2:56
I see seven questions here. Depending on the level of the answer desired, I can suggest (close to) seven different textbooks, each one of which will answer all seven of these questions and do them justice. But, in each case, it will take nearly the entire book to do so. That said, you might browse our regression tag to start. :-) –  cardinal Sep 7 '12 at 2:59
why are you linking to browse highly advance info??? that's not what's needed. other than that, fine, just a concise answer to the main question that would actually be helpful. –  kittensatplay Sep 7 '12 at 3:00
to address the specific questions in red: (1) regression tells you how the average value of the dependent variable changes as the related variables are changed. (2) conditional distributions are probability distributions for random variables when values of related variables or specific events are known to have occurred. The regression function is an average for Y based on the conditional distrbution for Y given the X variables are known to take on specific values. (3) I have already explained what the regression function estimates. –  Michael Chernick Sep 7 '12 at 4:37

## closed as not a real question by gung, cardinal♦, Peter Ellis, mbq♦Sep 7 '12 at 13:32

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I don't completely agree with the given answers. Regression is a statistics problem that goes back to Galton in the 19th century. One of his early examples was to relate the height of fathers with the height of their grown sons. Galton coined the term regression: meaning regression toward the mean. What he observed was that if you look at tall fathers their sons will tend to also be taller than average but not as tall as their fathers. Also short fathers will have short sons but their sons will tend to be taller than their fathers. Hence regression toward the mean. The sons of fathers of a given height will tend to be closer to the mean value in height.

There is an apparent paradox called the regression fallacy. If we turn the problem around and look at the tall sons and ask what the height of their fathers is it? Father's height will turn out to be taller than average but not as tall as the son. There is really no contradiction here.

In statistics simple regression estimates the function f(x) that is the average of a variable Y given the Value of the variable X is x. The function f(x) is called the regression function and it is estimated based on a sample of paired values for X and Y.

Simple regression has been generalized to multiple regression where we consider the average Y given several predictors X$_1$, X$_2$, ..., X$_p$ and the regression function becomes f(x$_1$,x$_2$,...,x$_p$) the average of Y given X$_1$=x$_1$, X$_2$=x$_2$,...X$_p$=x$_p$. The model is fit using sets of p+1 dimensional vectors of observations (y$_i$, x$_1$$_i, x_2$$_i$,...,x$_p$$_i$) for i=1,2, 3,...,n.

Linear regression refers to the case where f is linear in the coefficients of the predictor variables. The regression function for Y with p predictors X$_j$ j=1,2,..p is a linear function in the case where the joint probability distribution for Y and the X$_i$s is multivariate normal. Under the assumption that observed Ys differ from the regression function by a random normal error term with mean 0 and a constant variance and the X$_i$s are observed without error, the estimate of the parameters that minimize the squared deviations in the Y direction is "best" in the sense that it is the maximum likelihood estimator. These estimates are called least square estimates.

When the error terms are not normally distributed there are alternative (so-called robust) estimators that are better than least squares. When the Xs have error in their measurement the problem is called "error in variables regression" (aka Deming regression).

The regression function can also be nonlinear in the parameters and in that case we call the problem a nonlinear regression problem. This problem can be solved by the method of least squares. However in the linear case there is a nice closed form solution while in nonlinear regression numerical methods are usually needed to get the solution.

That is regression in a nutshell that is hopefully understandable.

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the stanford phd, best of all, couldnt ask for more –  kittensatplay Oct 7 '12 at 7:26

Regression is a broad term describing many different ways to investigate how one thing depends on other things. For example regression might be used to see how smoking affects your chance of getting cancer or how well a crop grows depending on the amount of fertiliser and water used.

Sub Questions

What is the purpose of regression?

To learn about the relationships involved so that the dependant quantity can be, for example, forecast or optimised given the other quantities.

Why do we need it?

Because otherwise we'd be stuck with opinions and superstition when it comes to determining the relationship between things.

The rest of the sub questions have been answered above, apart from the 'web calculator'. Regression is too broad a term for it to be possibly covered by a single calculator. There are probably simple web calculators out there for some types of regression, such as linear regression.

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For those older than 7, I have somewhat conflated causation and correlation in the above answer for the purpose of extreme simplicity. I hope this is an acceptable compromise in the circumstances. –  Bogdanovist Sep 7 '12 at 3:14
I think your answer is pretty good +1. I do think you missed mentioning something important about regression, namely that it is a function giving the conditional average for the dependent variable when the values of the indeoendent variables are given. That distinguishes it from other functions that could be used to relate variables. –  Michael Chernick Sep 7 '12 at 5:03
Sure, if you can re-word that for a 7 year old I'll register 10 accounts and they can all give you +1 :). Less factiously, I was trying to circumvent that by answering in such as way as to not require understand of what a function is at all. You always lose something when you simplify. –  Bogdanovist Sep 7 '12 at 5:08
I think you were up for the challenge with many of your answers to high's questions. Maybe it was a minor point but important in my view. To keep on the 7 year old level perhaps you could have said that the regression is a special function that represents how the average value for Y changes when we know the values of the Xs. –  Michael Chernick Sep 7 '12 at 5:20

Here's the way I explained it to my kids (ages 7 and 9). Regression is about the way two measurements change together. Like if we want to make a prediction (they seem to understand and like making "predictions"). If a classmate's height goes up 1", how much does his weight go up? Then I wrote it out in an equation and talked a little about using a variables to represent numbers, etc, but heck, even the 9 year old hasn't had algebra yet. I left it at regression is figuring out how much the weight goes up when the height goes up.

I didn't get into all that other stuff - when we start talking about math I know I generally have 3-5 minutes to get one or two facts in there, and I want to always leave them wanting more.

My apologies if you didn't literally mean so a 7 year old can understand it.

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