A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

ALGEBRA HELP- Does anyone with patience know to do the “Least Squares Linear Regression Method”? I watched a YouTube video on how to do it but I don’t know how to apply it here. Sorry this one is long…and I really want to understand all of it, but if you can help with even one part- please do. The table lists the distances (in megaparsecs; 1 megaparsec= 3.085 × 10^24 cm, and 1 megaparsec= 3.26 million light-years) and velocities (in kms per second) of four galaxies moving rapidly away from Earth. (I’ll put the table in the comments) (a) Plot the data using distances for the x-values

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    (cont.) and velocities for the y-values. What type of relationship seems to hold between the data? (b) Find a linear equation in the form y=mx that models these data using the points (520, 40,000) and (0, 0). Graph your equation with the data on the same coordinate axes. (c) The galaxy Hydra has a velocity of 60,000 km per sec. How far away is it according to the model in part (b)? (d) The value of m is called the Hubble constant. The Hubble constant can be used to estimate the age of the universe A (in years) using the formula A= (9.5)(10^11)/m (e) Astronomers currently place the value of the Hubble constant between 50 and 100. What is the range for the age of the universe A?

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1437111756117:dw|

  3. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    No one brave enough to tackle this one? lol

  4. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Did you want to go through all the parts?

  5. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    This actually doesn't look too bad. I'm assuming that your class wants you to do this by hand?

  6. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes. I know it should be easy which makes me feel stupid for asking...

  7. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    No, no worries. It's only easy because I've had to pull my hair out on these in the past.

  8. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Have you already gone ahead and graphed the data for part a)?

  9. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes. I dont see the relation though

  10. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    OK, I'm going to go ahead and use technology on my side to see the graph. Hold on one moment.

  11. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Alright, thank you!

  12. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    OK, here's what I see:

    1 Attachment
  13. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Your graph is much more proportional than mine,haha, and I see the curve now

  14. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Well, I cheated with technology. :) Alright, so we see the curve now.

  15. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    It's actually very straight, so a line should do a good approximation.

  16. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So its linear? is that the relationship?

  17. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yep, one of the few words in math that actually makes some sense. :)

  18. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Alright, so now for part b).... whoa, hang on... this is a lot simpler than least square regression... you won't need that level of complexity...

  19. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So how do we make this into a linear equation? Take a random pair of coordinates?

  20. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yeah I don't know. Our teacher had as watch a video about it before answering this question.

  21. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yeah, probably not needed for this one at least... your intuition into taking a random pair of coordinates is the best move. Actually the question says to use the points (520,42000) and (0,0)

  22. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So, they've chosen the random points for us.

  23. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So, part b) wants us to write something for y = mx. The main challenge right now is to find m, the slope. Do you have any ideas based on the points they gave us?

  24. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So, 420000=m(520) Because you're just subracting the first coordinantes by the second pair which are zeros

  25. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    OK, looks good

  26. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So, m=807.692

  27. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I think you mean 80.769, I believe it was 42,000 vs. 420,000, but I might be mistaken.

  28. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Actually, wait... The points were (0,0), and (520,40,000) typo on my part. Sorry.

  29. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oops it was 40,000. Guess we dragged the 2 from 520 by mistake

  30. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yep, that happened. :) So, I'm getting 76.923

  31. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah haha. So 40000=m(520) So m=76.923

  32. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yay!!

  33. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So our equation is y = 76.923 x, where x is the distance and y is the velocity.

  34. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I'll go ahead and plot this over my previous graph, one second.

  35. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Here we go

    1 Attachment
  36. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So for part C, I plug in the velocity and y=(76.923)(60,000) ?

  37. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Careful... the velocity goes into the y, not the x.

  38. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Almost linear, do I needto change answer A?

  39. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Actually it would be a good idea to write your equation as: v = 76.923 d to keep that clear.

  40. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    No need to change your answer. In the real world, there is almost NOTHING that is perfectly described by an equation. It is "close enough" so we would say it is linear.

  41. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Actually, this equation does an amazing job of fitting the data, and any scientist would be very happy with this. :)

  42. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay, then linear it is. And galaxy Hydra is 780 (megaparsec?) away?

  43. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Let me check.

  44. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yep, I agree.

  45. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Now to estimate the age of the universe with our slope.

  46. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Does the m stand for megaparsec?

  47. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I don't think so, mega is usual a capital M in science. So I'm pretty sure they are referring to m as in the slope of the line. Also, is the formula written like this? \[\frac{9.5 \times 10^{11}}{m}\]

  48. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

  49. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    OK, I think all they want is to just plug in our m = 76..... into the equation.

  50. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Do I have to simplify it at all?

  51. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Sure, it will be easier to understand that way... you'll need a powerful calculator though. Your computer calculator can probably handle it or ask google. :)

  52. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I'm getting a really big number...

  53. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Me too :(

  54. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I'm using mathway, what are you using?

  55. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Just searching directly in Google the following 9.5*10^11 / 76.923 gives me this 12350012350

  56. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Looks like it has a built in calculator, this agrees with my other one, it just dropped a few decimals.

  57. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I got 12348888600.026 so... 1.23x10^11 ? Does that sound reasonable?

  58. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Sure, our model isn't perfect anyway, so that's a good estimate.

  59. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So I have no lead for what part E wants me to do

  60. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Just real quick I think you want 1.23x10^10

  61. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh okay. Sounds good. Good to double check, ty

  62. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    OK, so E is just a really complicated way of them telling you to do part D again. Except this time use m = 50 and see what you get. Then use m = 100 and see what you get. Then you'll see that this is a range of possible ages for the universe. m = 50 gives the maximum age and m = 100 gives the minimum age.

  63. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ohhh okay!! Thank you so much!!!

  64. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Your welcome! Not so bad hopefully! :)

  65. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Not as bad as I thought it would be at all XD guess I'm just afraid of big numbers

  66. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    They are scary, but we can still deal with them. Just takes more paper and typing. :) Good work! Take care!

  67. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    If you want me to check the other two answers you get, just let me know. In fact, I'll post mine below so you can double check.

  68. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    m = 100 -> 9,500,000,000 = 9.5 x 10^9 m = 50 -> 19,000,000,000 = 1.9 x 10^10

  69. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes! B) Yay team! Have a good *enter time of the day here*

  70. jtvatsim
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    lol Sounds good, you too!

  71. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.