Search Results

To get $\beta$ instead of $b$, all you have to do is standardize your $x$ and your $y$ are run a regression of the standardized $y$ on the standardized $x$. … Then run the regression:$$\tilde{y}=\tilde{x}b+u$$ and you will estimate the slope paramter in standard deviation units. …

I think I figured the answer out. Ultimately, I am trying to compare the partial $R^{2}$ to the coefficient. They are in some ways related. Consider we have a model:$$y=x\beta+\epsilon$$ where $x$ …

Consider the linear regression model:$$y=\beta_{0}+\beta_{1}x+u$$ The OLS estimators minimze the squared sum of residuals. …

Consider that we have the following time series of observations: $C_{t},I_{t},G_{t},X_{t}-M_{t}$ Now, $Y_{t}$ is defined as:$$Y_{t}=C_{t}+I_{t}+G_{t}+X_{t}-M_{t}$$ If we were to run a regression of …

Think of a linear regression model: $$ Y=X\beta+\epsilon $$ where $\epsilon|X\sim N\left(0,\sigma^{2}\right)$. The vector of parameters $\beta$ can be consistenly estimated by OLS. …

I have a question regarding linear regression that has been confusing me for some time. … Consider the linear regression model in matrix notation $$Y=X\beta+\epsilon$$ Consider now the OLS estimator that can be derived from the moment condition:$$E[X'\epsilon]=0$$ Now, we can write the vector …

Pooled OLS regressions in the case of Panel Data are usually frowned upon.First, if the conditional exogeneity condition holds, that is: $$ E[(\alpha_{i}+u_{it}|X_{it})]=0 $$ holds, then you might as …

There are formal tests for normality- in particular the Jarque-Bera/Skewness-Kurtosis type tests.

I got it after thinking it through. Of course, in both cases, the marginal effect of $x_{1}$ is the same for a given value of $x_{1}$ and $x_{2.}$ The difference is that the second model includes s …

Consider the regression model:$$y=x\beta+u$$ Let us take expectations:$$E[y]=E[x\beta+u]=E[x\beta]$$ by linearity of the expectations operator and $E[u]=0$ . …

Consider the following model:$$y=x\beta+u$$ Now, let us take conditional expectations, assuming conditional exogeneity, such that $$E[u|x]=0$$ $$E[y|x]=\beta E[x|x]=\beta x$$ By the Law of Iterated …

As the RHS variables are generated by OLS, they are actually "generated regressors". It is perfectly fine to estimate the model by OLS, but you have to adjust standard errors. The classic paper by Pag …

Now, I wish to run a regression, say of ${HH}_{t}$ (or the HH index on time $T)$ on a particular set of world characteristcs, call it $X_{Wt}$. … The regression is: $$ {HH}_{t}=\alpha+\beta X_{Wt}+\epsilon_{t} $$ Now, in the above, the problem is that every year, the total number of countries is changing. …

Consider a regression model:$$y=x_{1}\beta_{1}+x_{2}\beta_{2}+u$$ Now, consider a different regression model:$$y=\frac{x_{1}}{x_{2}}\gamma_{1}+x_{2}\gamma_{2}+v$$ Of course, in the second model, the … I mean whenever I think of linear regression, I always think of it as holding the value of an included regressor constant. …

Consider the following Linear Regression Model. …