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## Get ready for AP® Statistics

### Unit 3: Lesson 2

Estimating with trend lines- Estimating the line of best fit exercise
- Eyeballing the line of best fit
- Estimating with linear regression (linear models)
- Line of best fit: smoking in 1945
- Estimating slope of line of best fit
- Estimating equations of lines of best fit, and using them to make predictions
- Equations of trend lines: Phone data

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# Estimating the line of best fit exercise

CCSS.Math: , ,

Sal solves a problem where he has to estimate the line of best fit for a scatter plot. Created by Sal Khan.

## Want to join the conversation?

- I love Khan academy :)))!(6 votes)
- i am lost. when i do it on the practice, i am usually wrong by one or two points. is there a way to calculate this??halp!(2 votes)
- Here's a process you might try. Find the point that is the closest to one corner. Then, find the point that is closest to the opposite corner. Connect those two points.

Then, look at the line you draw and compare the rest of the points to it. If there are more points above the line than below it, then you might need to move the line up some. And if there are more points below the line than above, you might need to move the line down some.

Just experiment until you've got the line as close as possible to as many points as you can. It's OK if some points are far away, as long as your really close to most of the points.(7 votes)

- Can you have a line of best fit when you have no correlation?(4 votes)
- If the correlation is exactly 0, then the best fit line using least squares regression is the horizontal line (slope 0) through y-bar (the mean y-value).(2 votes)

- How do we make predictions in scatterplots(4 votes)
- Honestly, I still don't get it. How would you know if it's accurate? And there's a method called Least Squares to find the equation, but how would you calculate if there are hundreds of points?(3 votes)
- If there are hundreds of points you not be using a line graph, you should be using a f/x table (frequency table)(1 vote)

- What does best line fit mean(3 votes)
- its the imaginary linear line that would go best in-between the points to show how good of a fit it is(1 vote)

- Where are these questions? Can I practice with them?(2 votes)
- I don't get what they mean by line of best fit? Can someone explain that to me, please?(1 vote)
- It means that a line that best represents a situation or problem(3 votes)

- Does the line of best fit have to have the same amount of points on each side?(1 vote)
- No, not necessarily. The line of best fit has to reach or be close to most of the points. So whether it does or does not have an equal amount of points on each side doesn't matter.(2 votes)

- does this make any sense to anyone?(2 votes)
- It actually makes sense after a while. If the dots all seem to be centered around a line, then that's the line of best fit. if they seem completely random, there is no line of best fit. Hope this helps a bit(1 vote)

## Video transcript

Find the line of
best fit, or mark that there is no
linear correlation. So let's see, we have
a bunch of data points, and we want to find a
line that at least shows the trend in the data. And this one seems
a little difficult because if we ignore these
three points down here, maybe we could do a line that
looks something like this. It seems like it kind of
approximates this trend, although this doesn't
seem like a great trend. And if we ignored these
two points right over, we could do something like
maybe something like that. But we can't just
ignore points like that. So I would say that
there's actually no good line of best fit here. So let me check my answer. Let's try a couple
more of these. Find the line of best-- well,
this feels very similar. It really feels like there's
no-- I mean, I could do that, but I'm ignoring
these two points. I could do something
like that, then I'd be ignoring these points. So I'd also say no good
best fit line exists. So let's try one more. So here it looks like there's
very clearly this trend. And I could try to fit it a
little bit better than it's fit right now. So it feels like something
like that fits this trend line quite well. I could maybe drop this
down a little bit, something like that. Let's check my answer. A good best fit line exists. Let me check my answer. We got it right.