Regressions with two independent variables where one is part of another.Probability with Independent Normal...

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Regressions with two independent variables where one is part of another.


Probability with Independent Normal VariablesUnderstanding Linear Regressions with Least SquaresOptimizing Independent Variables to Maximize Dependent VariableWorking with the sum of two independent random variables, and estimating a parameterProduct of two independent random variablesCovariance between two variables when one of the variables only has two possible valuesTransformation of independent variables in regression (Measurement Error)Correlation of two independent variablesA question regarding standardized regression coefficient in a regression model with more than one independent variableMultivariate linear regression with 2 independent variables - formulae













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$begingroup$


I am doing simple regression analysis where I use one-way fixed effect model to estimate the effects of two variables on dependent variable. The question I am asking is how to interpret these two variable's coefficients after regression if one is subset of another, e.g A is a part of B.



For example, I want to research how the growth of yearly purchases affected investment policy. And I am able to decompose the purchases on different types of purchases. Lets assume there are 10 types of purchases and I am interested particularly in type D purchases.



How do I interpret result if for example I would the regress investments policy on total purchases and D purchases growths, and then only D purchases growth.



I was told that if you have for D purchases growth coefficient (-/minus) then the effect of D purchases is less effective than total purchases; (+/plus) then it increases the effect of total purchases; (insignificant) then there is no effect outside total purchases.



Am I wrong? Is there any more convenient explanation of it? Could you help and explain, please?



Regression in Stata:



xtreg Invest L.(Invest D_purchases Leverage SizeAssets ROA TobinQ Tangible Growth), fe vce(cluster eTicker)



xtreg Invest L.(Invest Total_purchases D_purchases Leverage SizeAssets ROA TobinQ Tangible Growth), fe vce(cluster eTicker)










share|cite|improve this question











$endgroup$












  • $begingroup$
    Welcome at MathStackExchange(MSE)! You should consider adding your regression equation. Often one equation tells us more than a thousand words :D.
    $endgroup$
    – MachineLearner
    Mar 12 at 22:28










  • $begingroup$
    Hi Viadisiav. I am having trouble understanding your question. I think you have a lot of points $(x_i, y_i)$ where $x_i = (d_i, a_i)in mathbb R$ and $y_iin mathbb R$ and where $d_i$ is the growth of type D purchases, $a_i$ is the growth of all purchases, and $y_i$ is a real number representing "investment policy." Is that correct? You also talk about the "effectiveness" of the independent variables. Is the "effectiveness" of an independent variable the change in $r^2$ (the coefficient of determination) caused by that random variable?
    $endgroup$
    – irchans
    Mar 12 at 22:56


















1












$begingroup$


I am doing simple regression analysis where I use one-way fixed effect model to estimate the effects of two variables on dependent variable. The question I am asking is how to interpret these two variable's coefficients after regression if one is subset of another, e.g A is a part of B.



For example, I want to research how the growth of yearly purchases affected investment policy. And I am able to decompose the purchases on different types of purchases. Lets assume there are 10 types of purchases and I am interested particularly in type D purchases.



How do I interpret result if for example I would the regress investments policy on total purchases and D purchases growths, and then only D purchases growth.



I was told that if you have for D purchases growth coefficient (-/minus) then the effect of D purchases is less effective than total purchases; (+/plus) then it increases the effect of total purchases; (insignificant) then there is no effect outside total purchases.



Am I wrong? Is there any more convenient explanation of it? Could you help and explain, please?



Regression in Stata:



xtreg Invest L.(Invest D_purchases Leverage SizeAssets ROA TobinQ Tangible Growth), fe vce(cluster eTicker)



xtreg Invest L.(Invest Total_purchases D_purchases Leverage SizeAssets ROA TobinQ Tangible Growth), fe vce(cluster eTicker)










share|cite|improve this question











$endgroup$












  • $begingroup$
    Welcome at MathStackExchange(MSE)! You should consider adding your regression equation. Often one equation tells us more than a thousand words :D.
    $endgroup$
    – MachineLearner
    Mar 12 at 22:28










  • $begingroup$
    Hi Viadisiav. I am having trouble understanding your question. I think you have a lot of points $(x_i, y_i)$ where $x_i = (d_i, a_i)in mathbb R$ and $y_iin mathbb R$ and where $d_i$ is the growth of type D purchases, $a_i$ is the growth of all purchases, and $y_i$ is a real number representing "investment policy." Is that correct? You also talk about the "effectiveness" of the independent variables. Is the "effectiveness" of an independent variable the change in $r^2$ (the coefficient of determination) caused by that random variable?
    $endgroup$
    – irchans
    Mar 12 at 22:56
















1












1








1





$begingroup$


I am doing simple regression analysis where I use one-way fixed effect model to estimate the effects of two variables on dependent variable. The question I am asking is how to interpret these two variable's coefficients after regression if one is subset of another, e.g A is a part of B.



For example, I want to research how the growth of yearly purchases affected investment policy. And I am able to decompose the purchases on different types of purchases. Lets assume there are 10 types of purchases and I am interested particularly in type D purchases.



How do I interpret result if for example I would the regress investments policy on total purchases and D purchases growths, and then only D purchases growth.



I was told that if you have for D purchases growth coefficient (-/minus) then the effect of D purchases is less effective than total purchases; (+/plus) then it increases the effect of total purchases; (insignificant) then there is no effect outside total purchases.



Am I wrong? Is there any more convenient explanation of it? Could you help and explain, please?



Regression in Stata:



xtreg Invest L.(Invest D_purchases Leverage SizeAssets ROA TobinQ Tangible Growth), fe vce(cluster eTicker)



xtreg Invest L.(Invest Total_purchases D_purchases Leverage SizeAssets ROA TobinQ Tangible Growth), fe vce(cluster eTicker)










share|cite|improve this question











$endgroup$




I am doing simple regression analysis where I use one-way fixed effect model to estimate the effects of two variables on dependent variable. The question I am asking is how to interpret these two variable's coefficients after regression if one is subset of another, e.g A is a part of B.



For example, I want to research how the growth of yearly purchases affected investment policy. And I am able to decompose the purchases on different types of purchases. Lets assume there are 10 types of purchases and I am interested particularly in type D purchases.



How do I interpret result if for example I would the regress investments policy on total purchases and D purchases growths, and then only D purchases growth.



I was told that if you have for D purchases growth coefficient (-/minus) then the effect of D purchases is less effective than total purchases; (+/plus) then it increases the effect of total purchases; (insignificant) then there is no effect outside total purchases.



Am I wrong? Is there any more convenient explanation of it? Could you help and explain, please?



Regression in Stata:



xtreg Invest L.(Invest D_purchases Leverage SizeAssets ROA TobinQ Tangible Growth), fe vce(cluster eTicker)



xtreg Invest L.(Invest Total_purchases D_purchases Leverage SizeAssets ROA TobinQ Tangible Growth), fe vce(cluster eTicker)







statistics estimation linear-regression estimation-theory regression-analysis






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Mar 12 at 22:38







Vladislav Kolontai

















asked Mar 12 at 22:12









Vladislav KolontaiVladislav Kolontai

62




62












  • $begingroup$
    Welcome at MathStackExchange(MSE)! You should consider adding your regression equation. Often one equation tells us more than a thousand words :D.
    $endgroup$
    – MachineLearner
    Mar 12 at 22:28










  • $begingroup$
    Hi Viadisiav. I am having trouble understanding your question. I think you have a lot of points $(x_i, y_i)$ where $x_i = (d_i, a_i)in mathbb R$ and $y_iin mathbb R$ and where $d_i$ is the growth of type D purchases, $a_i$ is the growth of all purchases, and $y_i$ is a real number representing "investment policy." Is that correct? You also talk about the "effectiveness" of the independent variables. Is the "effectiveness" of an independent variable the change in $r^2$ (the coefficient of determination) caused by that random variable?
    $endgroup$
    – irchans
    Mar 12 at 22:56




















  • $begingroup$
    Welcome at MathStackExchange(MSE)! You should consider adding your regression equation. Often one equation tells us more than a thousand words :D.
    $endgroup$
    – MachineLearner
    Mar 12 at 22:28










  • $begingroup$
    Hi Viadisiav. I am having trouble understanding your question. I think you have a lot of points $(x_i, y_i)$ where $x_i = (d_i, a_i)in mathbb R$ and $y_iin mathbb R$ and where $d_i$ is the growth of type D purchases, $a_i$ is the growth of all purchases, and $y_i$ is a real number representing "investment policy." Is that correct? You also talk about the "effectiveness" of the independent variables. Is the "effectiveness" of an independent variable the change in $r^2$ (the coefficient of determination) caused by that random variable?
    $endgroup$
    – irchans
    Mar 12 at 22:56


















$begingroup$
Welcome at MathStackExchange(MSE)! You should consider adding your regression equation. Often one equation tells us more than a thousand words :D.
$endgroup$
– MachineLearner
Mar 12 at 22:28




$begingroup$
Welcome at MathStackExchange(MSE)! You should consider adding your regression equation. Often one equation tells us more than a thousand words :D.
$endgroup$
– MachineLearner
Mar 12 at 22:28












$begingroup$
Hi Viadisiav. I am having trouble understanding your question. I think you have a lot of points $(x_i, y_i)$ where $x_i = (d_i, a_i)in mathbb R$ and $y_iin mathbb R$ and where $d_i$ is the growth of type D purchases, $a_i$ is the growth of all purchases, and $y_i$ is a real number representing "investment policy." Is that correct? You also talk about the "effectiveness" of the independent variables. Is the "effectiveness" of an independent variable the change in $r^2$ (the coefficient of determination) caused by that random variable?
$endgroup$
– irchans
Mar 12 at 22:56






$begingroup$
Hi Viadisiav. I am having trouble understanding your question. I think you have a lot of points $(x_i, y_i)$ where $x_i = (d_i, a_i)in mathbb R$ and $y_iin mathbb R$ and where $d_i$ is the growth of type D purchases, $a_i$ is the growth of all purchases, and $y_i$ is a real number representing "investment policy." Is that correct? You also talk about the "effectiveness" of the independent variables. Is the "effectiveness" of an independent variable the change in $r^2$ (the coefficient of determination) caused by that random variable?
$endgroup$
– irchans
Mar 12 at 22:56












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