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Math Help - linear graph

  1. #1
    mat
    mat is offline
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    Exclamation linear graph

    I have to find how long it takes for boiling water to reach 70 degrees celcius i have collected data and put it in excel
    time (min) temp (celcius)
    0 101
    0.5 96
    1 93
    1.5 88
    2 85
    2.5 82
    3 80
    3.5 77
    4 75
    4.5 73
    5 71
    5.5 70
    6.5 69.5


    Excel got the equation line of best fit y=-5.01852x plus 96.824
    R squared=0.9433
    what do these mean?
    Is the line of best fit accurate and is there enough data to be based on a conclusion?
    Is this graph appropiate for a linear model?
    What do I write in the conclusion?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by mat View Post
    I have to find how long it takes for boiling water to reach 70 degrees celcius i have collected data and put it in excel
    time (min) temp (celcius)
    0 101
    0.5 96
    1 93
    1.5 88
    2 85
    2.5 82
    3 80
    3.5 77
    4 75
    4.5 73
    5 71
    5.5 70
    6.5 69.5


    Excel got the equation line of best fit y=-5.01852x plus 96.824
    R squared=0.9433
    what do these mean?
    Is the line of best fit accurate and is there enough data to be based on a conclusion?
    Is this graph appropiate for a linear model?
    What do I write in the conclusion?
    1. The R squared figure means that the data are an excellent fit to the regression line that Excel found (R squared =1 is a perfect fit).

    2. The equation can be rewritten in terms of time t and Temp T as:

    T=-5.01852 t + 96.824

    This line is the one you should use when predicting the temprature corresponding to a given cooling time.

    What you want is the line that gives the cooling time to a given temprature. You can get this by doing what you did before but with the columns reversed, when it will give you an equation which will be:

    t=aT+b

    where a and b are numbers given by the regression calculation.

    You can instead just rearrange the equation you already have, but it will not be as good at predicting the time to cool to a given temprature but that may not matter too much in this case.

    CB
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