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### Course: Statistics and probability>Unit 5

Lesson 3: Introduction to trend lines

# Line of best fit: smoking in 1945

The scatter plot shows how many adults in America smoked from year to year. We can guess how many smoked in 1945 by drawing a line that slopes down through the points. Then we see how high the line would be 20 years earlier. 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%).
• why is smoking in 1945?
• to improve morale and decrease boredom during the war
• Confusing because it started in 1945