So let's let Y be the ith child's height and Xi be the ith's parents height.

Now we want to find the best line, where we want the line to look like child's

height is an intercept, which let's label beta nought plus the parent's

height times a slope, which we're going to label beta one.

So beta nought and

beta one are parameters that we would like to know that we don't know.

Well, we need a criteria for the term best.

We need to figure out what we mean by the best line that fits the data.

Well, one criteria is the famous least squares criteria.

And the basic gist of the equation is we want to minimize the sum of the squared

vertical distances between the data points, the height of the data points,

the child's heights and the points on the line, on the fitted line.

And we can write this as summation Yi,

the child's heights minus beta nought plus beta 1Xi,

where that particular parent's heights would put them on the fitted line.

We'll go through this a lot and hopefully, you'll get the hang of it.

And then later on at the end of the lecture, I'll actually show you

the math of how we can come up with the solution for those that are interested.

Let's talk about what our equations mean with a picture.

Here's a dataset.

What our least squares criteria to find the best re,

regression line is going to do is, it's going to take each point.

So for example, take this point right here.

That's the point x1, y1 and this might be the point x2,

y2 and this might be the point xn, y,n.

It's going to take all these points and fit a line through the data.