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Math Help - linear regression

  1. #1
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    linear regression

    According to the US Bureau of the Census, Statistical Abstract of the United States, 1994, the population of the state of Wisconsin in thousands is as given in the table below:
    Year Population
    (in thousands)

    1970 7432
    1980 9438
    1990 12104
    2000 14102

    Lex x represent the number of years since 1970.
    1) Find the equation of the line representing this relationship using linear regression.
    y=ax+b

    y=226.76X + 7367

    2) Use this equation to predict the population of Wisconsin in the year 2010.

    y=226.76(4) +7367
    y=907.04 +7367
    y=8274.04

    Let me know if I am way off here please
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by jccurtis
    According to the US Bureau of the Census, Statistical Abstract of the United States, 1994, the population of the state of Wisconsin in thousands is as given in the table below:
    Year Population
    (in thousands)

    1970 7432
    1980 9438
    1990 12104
    2000 14102

    Lex x represent the number of years since 1970.
    1) Find the equation of the line representing this relationship using linear regression.
    y=ax+b

    y=226.76X + 7367

    2) Use this equation to predict the population of Wisconsin in the year 2010.

    y=226.76(4) +7367
    y=907.04 +7367
    y=8274.04

    Let me know if I am way off here please
    Regression line equation not checked, but looks OK

    The last calculation should go more like:

    y=226.76(40) +7367
    y=9070.4 +7367
    y=16437.4

    RonL
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  3. #3
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    Since population tend to grow exponentially, I'd use EXP to estimate the population in 2010 instead of linear regression...

    LastData = FirstDate*Exp(Tr)

    14102 = 7432*EXP(4r)
    r=ln(14102/7432)/4
    r=16%

    So the average growth rate for every 10 years is 16% and the population in 2010 should be somewhere around:

    Pop_2010 = 7432*Exp(5*0.16)
    Pop_2010 = 16551
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by cmart022
    Since population tend to grow exponentially, I'd use EXP to estimate the population in 2010 instead of linear regression...

    LastData = FirstDate*Exp(Tr)

    14102 = 7432*EXP(4r)
    r=ln(14102/7432)/4
    r=16%

    So the average growth rate for every 10 years is 16% and the population in 2010 should be somewhere around:

    Pop_2010 = 7432*Exp(5*0.16)
    Pop_2010 = 16551
    1. The data when plotted show no sign of exponential growth, so despite
    the growth of populations when not constrained usually being modelled
    this way there is no need here. But there is no reason why not except:-

    2. The question asks for a linear fit.

    3. You are using only two of the data points. If you are going for an
    exponential model you should do a non-linear regression (or linear regression
    on the log population) using all the data (as this is an exercises in regression).

    RonL
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