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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. …

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. …

Consider a linear regression model, wherein: $$ y_{i}=x_{i}\beta+\epsilon_{i} $$ where notation is standard and $x$ is a scalar. …

Consider the linear regression model $$y_{i}=x_{i}'\beta+\epsilon_{it}$$ where we have assumed that the model is linear in its parameters. …

When we estimate a linear regression model, say we obtain an estimate for \beta as $\hat{\beta}=(x'x)^{-1}(x'y)$ , the standard least standard least squares solution. …

Consider we have the following regression model: $$y_{it}=x_{it}'\beta+\alpha_{i}+\upsilon_{it}$$ where we have data on $N$ individuals for $T$ time periods. …

I have a question about linear regression in general. …

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 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 …

Consider the following Linear Regression Model. …

Consider the linear regression model: $$y_{it}=x_{it}\beta+\epsilon_{it}$$ where $x$ is single regressor. …

Consider the following regression model$$y_{it}=\beta_{1}M_{i}+\beta_{2}F_{i}+x_{it}'\gamma+\epsilon_{it}$$ where the LHS is some individual specific, time varying regressand the RHS variables consist … It is clear that if $x_{it}$ was not present, an OLS regression of the LHS on the RHS would result in the estiamtes representing conditional means by groups. …

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 …

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 …

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 $E[u]=0$ . …