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Rexy Bandiola
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Tyro
Asked: 2021-04-08T05:53:09+00:00 In: ,

linear regression

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provide an answer that being showed in the picture.

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  2. acedstud
    This answer was edited.

    First, let’s complete the table.

    Thus,

    x y x^2 xy
    1 25 1^2=1 1\times25=25
    2 30 2^2=4 2\times30=60
    3 32 3^2=9 3\times32=96
    4 45 4^2=16 4\times45=180
    5 50 5^2=25 5\times50=250
    \sum{x}=15 \sum{y}=182 \sum{x^2}=55 \sum{xy}=611

    a=\dfrac{(\sum{y})(\sum{x^2})-(\sum{x})(\sum{xy})}{n(\sum{x^2})-(\sum{x})^2}=\dfrac{(182)(55)-(15)(611)}{5(55)-(15)^2}        [\because n is the number of observations, which is 5 in this case.]

    =\dfrac{10010-9165}{275-225}=\dfrac{845}{50}=16.9

    b=\dfrac{n(\sum{xy})-\sum{x}\sum{y}}{n(\sum{x^2})-(\sum{x})^2}=\dfrac{5(611)-(15)(182)}{5(55)-(15)^2}

    =\dfrac{3055-2730}{275-225}=\dfrac{325}{50}=6.5

     

    The equation of the line of best fit of linear regression is given by y=a+bx\Rightarrow y=16.9+6.5x.

    To find the number of members the club will have 5 years from now, note that in five years from now x=10, thus y=16.9+6.5(10)=16.9+65=81.9\approx82 members.

    Therefore, five years from now, we expect the club to have about 82 members.

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