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Math Help - I have given up on this question...help anyone

  1. #1
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    I have given up on this question...help anyone

    An experiment is performed to measure the dependence between solubility of a chemical in water and the temperature of the water. The following results are obtained:

    Temperature, x (oC) 0, 0, 0, 10, 10, 10, 20, 20, 20
    Solubility, y (g/litre) 4.8, 4.5, 4.6, 10.3, 10.5, 10.3, 16.4, 17.8, 15.9
    Temperature, x (oC) 30, 30, 30, 40, 40, 40, 50, 50, 50
    Solubility, y (g/litre) 22.1, 23.6, 23.2, 28.9, 29, 28.1, 34.5, 35.2, 35.8

    1)Fit a linear model to the data by estimating the parameters α and β.

    2)A chemical process is to run at 16oC. Find a 95% confidence interval for the expected solubility of the chemical at this temperature.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by goaway716 View Post
    An experiment is performed to measure the dependence between solubility of a chemical in water and the temperature of the water. The following results are obtained:

    Temperature, x (oC) 0, 0, 0, 10, 10, 10, 20, 20, 20
    Solubility, y (g/litre) 4.8, 4.5, 4.6, 10.3, 10.5, 10.3, 16.4, 17.8, 15.9
    Temperature, x (oC) 30, 30, 30, 40, 40, 40, 50, 50, 50
    Solubility, y (g/litre) 22.1, 23.6, 23.2, 28.9, 29, 28.1, 34.5, 35.2, 35.8

    1)Fit a linear model to the data by estimating the parameters α and β.

    2)A chemical process is to run at 16oC. Find a 95% confidence interval for the expected solubility of the chemical at this temperature.
    1) You are asked to do a linear regression analysis, so do it.


    CB
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  3. #3
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by goaway716 View Post
    An experiment is performed to measure the dependence between solubility of a chemical in water and the temperature of the water. The following results are obtained:

    Temperature, x (oC) 0, 0, 0, 10, 10, 10, 20, 20, 20
    Solubility, y (g/litre) 4.8, 4.5, 4.6, 10.3, 10.5, 10.3, 16.4, 17.8, 15.9
    Temperature, x (oC) 30, 30, 30, 40, 40, 40, 50, 50, 50
    Solubility, y (g/litre) 22.1, 23.6, 23.2, 28.9, 29, 28.1, 34.5, 35.2, 35.8

    1)Fit a linear model to the data by estimating the parameters α and β.

    2)A chemical process is to run at 16oC. Find a 95% confidence interval for the expected solubility of the chemical at this temperature.
    If you have ever used SAS(Statistical Analysis Software) or even MS-EXCEL(if you haven't heard of SAS), then this question should be a piece of cake!

    Your linear model should look like this:

    y = \alpha +  \beta x ; where y is the solubility and x is the temperature, α is constant and β is the parameter estimate for x(temperature). If β is positive, then with every unit increase in temperature, the solubility is predicted to be β units higher, holding other variables constant, and vice versa.

    for confidence intervals, you need to have a nice look at your textbook!
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