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Thread: Linear R^2 Values as Percent Weights for Multiple Variable Formula?

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    Linear R^2 Values as Percent Weights for Multiple Variable Formula?




    Hey guys,

    Statistics is not my strong suit.. The closest I've been to statistics is a college level Biology II class I took three years ago.. But I'm trying to learn. I have a website and two mobile apps where I've been collecting data from people for the past 5-6 months and would like to know how to make a weighted formula based on the linear regression analysis of 4 independent variables and 1 dependent variable.

    I'm using OriginPro 8.5.1. With the linear regression I've done on these 4 variables, the p values are all below 0.05 and it gives me the Adj. R^2 values for each one; which is all fine and dandy.

    I then take these 4 variables and perform a multiple linear regression analysis. The p value for this regression is 0.01-something and the highest value in the correlation table is 0.21 (Body Fat (Lbs) vs. Metabolism (Scale 1-5)). It also gives me the weighted y formula for this. But this is where I run into a problem, I think..

    I would like to output the results with Confidence Intervals (90%, 75%, 50%, 25%, 10%). Is there a way to do this with multiple linear regression? I couldn't figure out how to do that with OriginPro, if it's even possible..

    So this is what I've been doing with linear regression instead: (just with those 4 independent variables)
    -Verify that p < 0.05.
    -Write down Adj. R^2 value.
    -Determine what the y=mx+b formulas are for each variable at the 90%, 75%, 50%, 25%, and 10% Confidence Intervals. I figure these out with box plots. It results in 4*5=20 formulas.
    -Then I make one multi variable formula for each Confidence Interval using the Adj. R^2 values as a percent weight...

    Is that last step even remotely correct? For example, if the R^2 values for these 4 variables are 0.2, 0.3, 0.4, and 0.5, then this means the the percent weights would be 0.14, 0.21, 0.29, and 0.36. This would result in a formula that looks something like the following at each Confidence Interval:

    y=((mx1+b1)*0.14)+((mx2+b2)*0.21)+((mx3+b3)*0.29)+((mx4+b4)*0.36)

    Is this right? If not, am I on the right track? I can't seem to find the answer with the searches I've done here with "weight multiple regression" or on google. Am I using the correct terminology by using percent weights or is it called something else? I can't believe that I haven't found the answer to this question that must have already been asked and answered..

    Thanks,
    j

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    Re: Linear R^2 Values as Percent Weights for Multiple Variable Formula?


    Quote Originally Posted by 7rashcan View Post
    So this is what I've been doing with linear regression instead: (just with those 4 independent variables)
    -Determine what the y=mx+b formulas are for each variable at the 90%, 75%, 50%, 25%, and 10% Confidence Intervals. I figure these out with box plots. It results in 4*5=20 formulas.
    I don't think I've seen this, can you explain? The formula at 90% Confidence interval, differs from the formula at 10% confidence interval?

    I don't use OriginPro. But when I do a linear regression, I get m, and standard error.

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