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Math Help - Linear regression

  1. #1
    Ash
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    Linear regression

    I'm not sure if I did problems 1 and 3 correctly and I am not sure about how to do the others. I want to make sure I am answering them correctly in the right context.

    Problems 1-5, consider the following. From 1986 to 1998, the number of pairs of bald eagles was recorded every two years. The data is reported in the table below.






    1. Find the linear function y= mx + b that best models the data.

    When I used the linear regression on the calculator I got :

    Y = ax+ b

    a = 326.3
    b= -646150.6


    When I wrote it out, the answers are m= 4449-1875/1994-1986= 2574/8 = 321.8
    m=321.8

    Is that what they wanted me to find?


    2. Interpret the slope of the line you found in Problem 1.



    3. According to your model how many pairs of bald eagles were there in
    2000?

    When I used calculator : y= 6449.4


    When I wrote it out:
    y= mx = b
    y= 321.8 (2000)+B
    B= -637220.2
    y=6379.8




    4. According to your model, when will there be 10,000 pairs of bald eagles?




    5. In 1963, there were 417 pairs of bald eagles. How well does the function
    in Problem 1 model the data for that year?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Ash View Post
    I'm not sure if I did problems 1 and 3 correctly and I am not sure about how to do the others. I want to make sure I am answering them correctly in the right context.

    Problems 1-5, consider the following. From 1986 to 1998, the number of pairs of bald eagles was recorded every two years. The data is reported in the table below.






    1. Find the linear function y= mx + b that best models the data.

    When I used the linear regression on the calculator I got :

    Y = ax+ b

    a = 326.3
    b= -646150.6


    When I wrote it out, the answers are m= 4449-1875/1994-1986= 2574/8 = 321.8
    m=321.8

    Is that what they wanted me to find?
    The question wants you to perfoem a linear regression on the data. This is
    what is implemented in your calculator, but I expect that you are required
    to do this yourself. The details can be found here.

    2. Interpret the slope of the line you found in Problem 1.
    The slope in the average growth in the number of pairs per year.


    3. According to your model how many pairs of bald eagles were there in
    2000?

    When I used calculator : y= 6449.4
    Write it out using the m and b from you calculator, they are correct

    y = 326.3 2000 - 646150.6 = 6449.4


    4. According to your model, when will there be 10,000 pairs of bald eagles?
    You need to solve the equation:

    10000 = 326.3 y - 646150.6

    for the year y for this.

    5. In 1963, there were 417 pairs of bald eagles. How well does the function
    in Problem 1 model the data for that year?
    The model gives:

    326.3 1963 - 646150.6 = -5623.7

    for the number of pairs in 1963, which is absurd, and a poor fit with the
    given factoid.

    RonL
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