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### Course: 8th grade (Illustrative Mathematics)>Unit 6

Lesson 3: Lesson 4: Fitting a line to data

# Line of best fit: smoking in 1945

Sal estimates the percentage of American adults who smoked in 1945 using a scatter plot. Created by Sal Khan.

## Want to join the conversation?

• I don't understand this at all... can someone please explain this to me?
• We have a graph with various data points, and it looks like there is a linear relationship between the data points (because if you squint you can kinda see where a line could go, right in the middle of all the points).

Once you sketch this line, you know (even though you can't see it) that the line goes on forever in both directions. We know that 1965 on the graph is where x=0, and about 41 or 42% of Americans smoked... but we want to know how many Americans smoked in 1945.

Even though the graph doesn't show 1945, we can draw the line backwards (to the left of the y-axis) and estimate the y-value from the graph. In the video (at ) it looks like the y-value is about 51 or 52%.

Hope this helps a little!
• Is it possible to calculate a perfect line through the points?
• Only through some points. You can have a perfectly straight line when given only two points, but if there are more than two, most often a perfect line doesn't exist.
• Is there a way to make the equations easier to understand and do? I am good at drawing the line of best fit, but not the rate of change...
• Well, the rate of change is a slope which you need when drawing a line of best fit. You're just drawing a line that best fits the data.
• Is this a factual chart?
• I was wondering this too, so I looked it up and it's true that 45% of Americans smoked in 1965. What's interesting is that by 2015, the percentage had dropped and only 15% of Americans smoked.
• we continue the trend like that backwards, then is it possible to show that at some year ~100% population smokes?
• Assuming the trend stays exactly the same, then yes. You can continue the line for as far back and forward as it can go (from 0% to 100%).
• what if that estimate were to be a faction? And what would that fraction be?
• Confusing because it started in 1945
• are there any standard to how to get the "best" line ? how do you know that is the right line and this is not ?
• The best line has the most dots going in the same direction, if the line is wrong there would be outliers and you might not be able to use a line at all. I hope this helps!
• HOw do you approximately caculate the points in the first place.
• How are you supposed to determine where the line goes exactly? I've been doing some of the practice problems and have gotten every single one wrong because my line wasn't placed exactly where it showed in the hint section, and in result came up with a different answer.
• To figure out EXACTLY where the line goes, you'd have to check out some of Khan Academy's least square regression line (aka linear regression or LSRL) videos! The least square regression line is much more precise than the line of best fit, but the least square regression line is also MUCH MORE ADVANCED! It's in the AP Statistics curriculum!