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Scatterplots — Harder example

Watch Sal work through a harder Scatterplots problem.

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  • male robot hal style avatar for user Pure_Devotion
    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)
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  • leaf green style avatar for user Baukje Verwiel
    What's the second degree term he is talking about at ? And what is the coefficient? :)
    (8 votes)
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    • sneak peak purple style avatar for user Nur
      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)
  • leaf green style avatar for user Fatima ES
    What does he mean by "this term goes away and this term goes away" at ?
    (3 votes)
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    • duskpin tree style avatar for user Sarah K.
      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)
  • aqualine ultimate style avatar for user vmoney444
    Just wanted to say "Thank you Sal!" This was super helpful!
    (7 votes)
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  • leafers tree style avatar for user Akhil Nadigatla
    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)
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    • purple pi teal style avatar for user shreya21
      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)
  • leaf green style avatar for user purple05
    how do you know if its a line of best fit or a curve of best fit?
    (4 votes)
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    • male robot hal style avatar for user Panth Shah
      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)
  • duskpin ultimate style avatar for user Anmol Malhotra
    When x=0 , why Y not equal to 0? Please explain in detail
    (5 votes)
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  • blobby green style avatar for user jae.hodge
    how do you know your line of best fit is accurate?
    (2 votes)
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  • blobby green style avatar for user nazara sikdar
    what does increment means on y-axis and x-axis?
    (1 vote)
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    • duskpin tree style avatar for user Sarah K.
      "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)
  • mr pink red style avatar for user Ayesha Tauqeer
    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)
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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.