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    Interpreting the coefficients of my regression model




    Hi all,

    I am a student at Bournemouth University currently undertaking a research project into the pay-performance sensitivity in AIM companies. I want to investigate the impact of firm performance on total pay.

    My dependent variable is total pay (inc cash + equity pay) and my independent variable is firm performance. Data is for one year, 2013.

    Firm performance is measured in % e.g +10%, -13%. Total pay is measured to the nearest pound, e.g 761,376. However, both variables have been transformed via Log10 and were entered into the SPSS regression in their log form.

    I have attached the coefficients table as an attachment below. The B values are Constant 5.903 and Firm Performance 0.451.

    For suitable comparsion with prior literature, if possible, I would like to know the following:
    -I want to find out what a 10% and 1% increase in firm performance would correspond to in % increase in total pay?
    -As well as this as firm performance increases by 1 unit, by how many s does total pay increase by?

    I apologise in advance if I had not provided the relevant information and thank you for any help you could give me!

    Thanks

    George
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    Re: Interpreting the coefficients of my regression model

    Hello George,

    Firstly,

    Why did you have to transform the variables, was there anything wrong with the distribution?

    Secondly, as far as I remember to interpret the coefficients, say 10% increase in IV is associated with the mean difference in DV is: coefficient*ln10(1.1), i.e. 0.451*log(1.1)=0.0186, or for 1% - 0.451*log(1.01)=0.0019489

    Someone, please correct me if I not correct here.

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    Re: Interpreting the coefficients of my regression model

    Hi, thanks very much for your response.

    I transformed the variables because they were positively skewed and therefore not normally distributed.

    thanks again!

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    Re: Interpreting the coefficients of my regression model

    Quote Originally Posted by george1660 View Post
    Hi, thanks very much for your response.

    I transformed the variables because they were positively skewed and therefore not normally distributed.

    thanks again!
    Yep, that's what I thought. However, did you run any normality tests to check that (e.g. Jarque-Bera, Shapiro-Wilk, or similar)?

    Also, an important point is that normality of the variables is not required, rather it is the normal distribution of the residuals (along with a number of other assumptions of OLS regression, in case that is what you are using for estimations). Please refer to this great paper: Williams, M. N., Grajales, C. A. G., & Kurkiewicz, D. (2013). Assumptions of multiple regression: correcting two misconceptions. Pract. Assess. Res. Eval, 18. (PDF: http://www.pareonline.net/getvn.asp?v=18&n=11).

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    Re: Interpreting the coefficients of my regression model

    Another point for you to consider: I don't know the details of your research, but it is common to have control variables to make sure that the relationship you are attempting to test (i.e. new variable impact on DV) is indeed significant. Just by itself, you IV may be a significant predictor, but adding another variable can easily show you an opposite result.

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    Re: Interpreting the coefficients of my regression model

    Thanks again Kiton!

    I used the Shapiro-Wilk test for my normality tests. Thanks for the link to that journal article, it has proved very informative and has hopefully helped with my understanding.

    Also I have used a number of corporate governance variables in my analysis such as age, tenure, board size, institutional ownership etc. I have run regression with just firm performance and then subsequently added the corporate governance variables into the equation.

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    Re: Interpreting the coefficients of my regression model


    Quote Originally Posted by george1660 View Post
    Thanks again Kiton!
    I used the Shapiro-Wilk test for my normality tests. Thanks for the link to that journal article, it has proved very informative and has hopefully helped with my understanding.
    Also I have used a number of corporate governance variables in my analysis such as age, tenure, board size, institutional ownership etc. I have run regression with just firm performance and then subsequently added the corporate governance variables into the equation.
    My pleasure to help. You are welcome to post the analysis results for the full model with control variables entered first, in case you need help interpreting those results. Other than significance of the effect and the beta coefficient, it is also good to examine the change in the percent of explained variation attributable for the variable of interest (delta R squared) and whether it is significant.

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