Main content

## SAT

### Unit 10: Lesson 3

Problem solving and data analysis- Ratios, rates, and proportions — Basic example
- Ratios, rates, and proportions — Harder example
- Percents — Basic example
- Percents — Harder example
- Units — Basic example
- Units — Harder example
- Table data — Basic example
- Table data — Harder example
- Scatterplots — Basic example
- Scatterplots — Harder example
- Key features of graphs — Basic example
- Key features of graphs — Harder example
- Linear and exponential growth — Basic example
- Linear and exponential growth — Harder example
- Data inferences — Basic example
- Data inferences — Harder example
- Center, spread, and shape of distributions — Basic example
- Center, spread, and shape of distributions — Harder example
- Data collection and conclusions — Basic example
- Data collection and conclusions — Harder example

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# Scatterplots — Harder example

Watch Sal work through a harder Scatterplots problem.

## Want to join the conversation?

- Your startup disk is full. If you dont know what this means, you haven't been paying attention to Sal. (Yeah, thats what i'm saying. Its not time to check your facebook.)(18 votes)
- What's the second degree term he is talking about at1:42? And what is the coefficient? :)(8 votes)
- Also, a highest degree term is the term with the highest power. It is NOT always second degree/squared since if there was a x^3, that would be the highest degree term. In this example of parabolas/quadratic, the highest power is the second degree. But it isn't always(6 votes)

- What does he mean by "this term goes away and this term goes away" at3:00?(3 votes)
- The first two terms in the equation have an x in them; more specifically they are being multiplied by an x. When you plug in zero for x, those terms get multiplied by zero. Anything multiplied by zero is zero, so the equation results 0 - 0 + 0.969. The zeroes (those first two terms) can "go away" because adding them does not change the value of 0.969.(11 votes)

- Just wanted to say "Thank you Sal!" This was super helpful!(7 votes)
- Hi everyone. I had a question concerning the idea of correlation in scatterplots: so if we refer to a correlation as being 'weak' or 'strong' does it signify the strength of the relationship i.e. how close the points are to the line of best fit - or does it refer to the gradient of the line of best fit (e.g. a small change in one variable causes a relatively large change in the other)? Thanks.(4 votes)
- The 'weak' or 'strong' of a correlation signifies the strength of the relationship, so if a correlation is referred to as strong, it means that all the points are close to or lie on the line of best fit.

Hope this helps!(6 votes)

- how do you know if its a line of best fit or a curve of best fit?(4 votes)
- When you are dealing with graphs with a parabolic shape (curve) then you would use a curve of best fit. When dealing with linear functions, (more or less), then you would use line of best fit. It all depends on what shape the points on the graph are taking.(6 votes)

- When x=0 , why Y not equal to 0? Please explain in detail(5 votes)
- how do you know your line of best fit is accurate?(2 votes)
- It's not accurate, it's just the average of all points. However, if a question asks you to find a point using the line of best fit or something like that, you can treat it as if it's accurate.(2 votes)

- what does increment means on y-axis and x-axis?(1 vote)
- "Increment" is the amount by which the numbers increase on the axes. On the y-axis in this problem, the increment is five : 0, 5, 10, 15, 20, 25, . . .. (You can see the numbers "skip-count" by five). On the x-axis, the increment is one: 0, 1, 2, 3, 4, 5, 6, 7, . . ..(3 votes)

- If we make a best fit line in a scatter plot, the equation of the line would be y=mx+c. How can we find the gradient(m) for the equation?(2 votes)
- pick two points on the line and plug them into the slope formula:

Y2-Y1/X2-X1(1 vote)

## Video transcript

- [Instructor] The
scatter plot drawn above, we'll take a look at it after we finish reading the question, depicts the average annual United States per capita consumption of
high fructose corn syrup between the years 1970 and 1985. Which of the following functions best describes the relationship shown? So when we look at the scatter plot, we see that it definitely looks like we could fit a parabola to it. We could find a curve of best fit, and that parabola might look something like this. Once again, I'm just kinda estimating it, trying to draw a parabola with my hand. This is gonna be a hand-drawn parabola, but it's gonna look something like that. And what they're saying is, look, they've given us some candidates,
some quadratic functions that would describe this curve of best fit or this parabola of best fit. And so which of these could it be? Well, there's a couple of things that you might immediately see. The first is is that a
couple of these choices have a positive coefficient
on the highest degree term, on the second degree term. And then the other ones,
have a negative coefficient on the highest degree term. Well, if you have a positive coefficient on the highest degree term,
on the second degree term, and if we were talking about a quadratic, you're going to have an
upward opening parabola, and if you had a negative coefficient, it would be a downward opening parabola. What we have here is clearly, it looks like the right half
of an upward opening parabola. So we could rule out the ones that would be downward opening. So we could rule out the ones that have a negative coefficient on the second degree terms. So let's rule those out right over here. And then when we look
at the remaining two, we see there's a fairly
dramatic difference in them. This is 201 versus .201. 264 versus .264. 969 versus .969. And so we could really look
at our curve right over here and get a sense of and test some points. So if you look at or maybe the easiest
way is to actually test when x is equal to zero. So when x is equal to zero, depending on how we draw our curve, our y is going to be pretty low. Our y is going to be close to zero. I'll just write is going to be close to zero. It's going to definitely be below five. It's gonna be probably
definitely below two. So let's see which of these
choices describe that. So when x is zero here,
this term goes away, this term goes away, and we're left with 0.969. So y would be, so this has
a point zero, 0.969 on it, which seems pretty close to our criteria that hey, we want when x is
zero y is pretty close to zero. Let's see this one. This choice right over
here, when x is zero, this term goes away, this term goes away. Y is 969. If you picked this choice right over, this is not close to zero. This actually would be off
the charts right over here, the point zero, 969. It wouldn't even fit on that graph. So you can definitely rule this one out, and we would be left with
that choice right there, and you can try other points, but that one would definitely
be the easiest to evaluate.