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Thread: Determining error in slope for linear regression (error probagation in x and y)

  1. #1 Determining error in slope for linear regression (error probagation in x and y) 
    Forum Freshman
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    Hello, I had done a lab on fluid dynamics and had taken measurement error in both the dependent and independent variables.
    Having done a linear regression, I was told to determine the friction factor which is the slope of the linear regression.

    Is there a way in excel to determine the error in slope? I had googled for a long time but the only I can find is standard deviation in slope which does not account for measurement errors.

    Thank you


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  3. #2  
    Forum Ph.D.
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    Standard deviation apples to the numbers (mathematics). Since the numbers are supposed to be measurements (I guess) - physical quantities, the error estimate would be given by the standard deviation.


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  4. #3  
    Forum Professor wallaby's Avatar
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    on top of that the standard deviation in the slope is not supposed to be the same as the measurement error.
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  5. #4  
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    Hmm, I dont think they are equivalent.

    For instance if my measurement of x is extreamly inaccurate, the error of the slope of x against y should be more than measurement of x which are perfect.

    Thank you nontheless for the reply.

    Is there anyway to capture this error that is propagated from the points to the slope?
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  6. #5  
    Forum Professor wallaby's Avatar
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    I'm having trouble understanding what you're asking in your last post, what do you mean by "capture" and propagation of error from the points to the slope?
    I thought i'd elaborate on why you should use the standard deviation to measure the error in the slope, hopefully there's at least one helpful sentence in this spiel.

    As the measurement errors are supposed to be random, i.e. not systematic, then it follows that if the experiment were to be repeated there is a probability that a different set of parameters for the model would be obtained from the slightly different data. If the theoretical model is accurate then a smaller measurement error should lead to a smaller variation in the values of the parameters, like slope, over multiple independent trials. But what does this mean for you?

    Well you've run an experiment and you've found the slope of a line of best fit to the data, by using statistical functions in Microsoft Excel by the sounds of it, now you're wondering how much the uncertainty in the measurements could affect this value for slope. Another way to ask this question is, if i run my experiment multiple times what range of values for the slope will i calculate 95% of the time, this is known as a confidence interval. Since the value you have obtained approximates the mean value of the slope, it follows that 95% of the time that the experiment is repeated the values of the slope will be greater than or less than the value you calculated by a factor of 1.96 times the standard deviation of the error, between the regression line and the measured values.

    That was really a whole bunch of stuff that you wouldn't need to know unless you're doing a course in statistical analysis, but it's the short version of the "why" in why would we use the standard deviation to measure the error in the value of the slope.
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