Results 1 to 6 of 6

Math Help - Finding a linear model.

  1. #1
    AMV
    AMV is offline
    Newbie
    Joined
    Sep 2011
    Posts
    4

    Finding a linear model.

    UPDATE: I got the answer, but I won't mess with the problem, in case others need it! I won't state the steps though, to stay in line with this sites cheating policy! (I believe that's right, anyways)


    Gasoline mileage of automobiles is influenced by the horsepower of the automobile. Below is a table of the data, use the data table to answer the following question:

    HP(x) 49|52|55|58|61|64|67
    MPG(y) 65.4|56.5|46.0|49.2|40.3|39.4|36.1

    QUESTION: Find a linear model that fits the data, round to four decimal places



    Just an FYI, I know how to find linear models, but this one has gotten me completely confused. I know I need to start off with finding the slope, which I've tried, and continued to get wrong (the answer is in the back of the book). Does it have something to do with the fact that the first difference isn't equally separated? Please Help!!
    Last edited by AMV; September 27th 2011 at 10:59 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,553
    Thanks
    1424

    Re: Please help, this Linear Model seems impossible to find!

    Quote Originally Posted by AMV View Post
    Ok, I really need someone to explain this to me step-by-step, PLEASE! I have literally worked on this problem for three days!! Even just trying it would be appreciated!


    Gasoline mileage of automobiles is influenced by the horsepower of the automobile. Below is a table of the data, use the data table to answer the following question:

    HP(x) 49|52|55|58|61|64|67
    MPG(y) 65.4|56.5|46.0|49.2|40.3|39.4|36.1


    QUESTION: Find a linear model that fits the data, round to four decimal places



    Just an FYI, I know how to find linear models, but this one has gotten me completely confused. I know I need to start off with finding the slope, which I've tried, and continued to get wrong (the answer is in the back of the book). Does it have something to do with the fact that the first difference isn't equally separated? Please Help!!
    What are you allowed to use? Are you supposed to plot the points on a scatterplot then draw a line that fits by hand and find its equation? Or are you supposed to use linear regression to find a least-squares-line? Or some other method?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    AMV
    AMV is offline
    Newbie
    Joined
    Sep 2011
    Posts
    4

    Re: Please help, this Linear Model seems impossible to find!

    I'm assuming that with this problem, linear regression. This is literally the only problem on our homework like this, so I really don't know what to do. But I know I must be missing a step and our book shows us how to use a graphing calculator, but my teacher wants us to do everything by hand, so I'm kind of stuck :\
    The answer is y= -1.5214x+135.8
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,553
    Thanks
    1424

    Re: Please help, this Linear Model seems impossible to find!

    Quote Originally Posted by AMV View Post
    I'm assuming that with this problem, linear regression. This is literally the only problem on our homework like this, so I really don't know what to do. But I know I must be missing a step and our book shows us how to use a graphing calculator, but my teacher wants us to do everything by hand, so I'm kind of stuck :\
    The answer is y= -1.5214x+135.8
    The least squares line is given by \displaystyle y - \bar{y} = b\left(x - \bar{x}\right), where \displaystyle b = \frac{\sum{\left(x - \bar{x}\right)\left(y - \bar{y}\right)}}{\sum{\left(x - \bar{x}\right)^2}}.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    AMV
    AMV is offline
    Newbie
    Joined
    Sep 2011
    Posts
    4

    Re: Please help, this Linear Model seems impossible to find!

    Well, I tried that, and I probably did something wrong... I got -2.96 for slope again. Ugh...

    The second part of the problem is to "Graph the model found in question 1 and the scatter plot of the data on the same axes. Discuss how good the model fits the data." If that helps at all..
    Follow Math Help Forum on Facebook and Google+

  6. #6
    AMV
    AMV is offline
    Newbie
    Joined
    Sep 2011
    Posts
    4

    Re: Finding a linear model.

    It took me a while but I think I figured it out! The missing step must have been the least squares part. I knew it was something little like that, that was throwing me off!

    So, thanks for the least squares reminder!

    Sometimes I just need to write the whole problem out to see what I'm doing wrong, and then...something just clicks. haha.

    P.S. this site is great to use, especially when my library's math help center isn't open!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Linear Damping Model
    Posted in the Advanced Applied Math Forum
    Replies: 4
    Last Post: June 22nd 2010, 03:59 AM
  2. Replies: 0
    Last Post: January 12th 2010, 02:40 PM
  3. Non-linear process model with Linear measurement model
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: September 1st 2009, 11:32 PM
  4. Replies: 3
    Last Post: April 15th 2009, 01:18 AM
  5. General Linear Model
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: March 12th 2009, 08:02 AM

Search Tags


/mathhelpforum @mathhelpforum