Linked Questions

I've come across some equations on regression coefficients for multiple linear regression(Fig.1 and Fig.2) with 2 independent variables and was wondering how they were derived. FIG.1 FIG.2 I'm aware ...

We consider the least square problem in the case where we got only one independant variable $x_i$ and only one dependant variable $y_i$. The number of observations is $n$. In the case of the linear ...

When we derive the estimates of $\vec{\beta}$ such that they minimize the sum of squared error ($SSE$) we begin with $\sum_{i=1}^{n} (y_i - (\beta_0 + \beta_1x_1 + ... + \beta_kx_k))^2$. This is ...

For simple linear regression, the regression coefficient is calculable directly from the variance-covariance matrix $C$, by $$ C_{d, e}\over C_{e,e} $$ where $d$ is the dependent variable's index, ...

Here is the formula of standardized regression coefficients. I have two questions: 1)How do we derive this formula? 2)How can we understand intuitively this formula(I cannot understand why do we ...

In a univariate regression, $Y=a+bX+e$, the solution for slope b is given by $COV(X,Y)/VAR(X)$. Is there a similar expression for a bivariate regression $Y=a+bX+cZ+e$. What is the closed form ...

Suppose I am trying to estimate a multiple linear regression with $k$ regressors and I have $n$ observations $$Y = X\beta + \epsilon$$ Where $\beta \in \mathbb{R}^k$ and $X \in \mathbb{R}^{k \times ...

Without using matrices How can you derive OLS estimators in multiple regression ?

So I'm trying to show that regressing y on x in this case (fixed effects model): $y_{it} = \beta x_{it} + \theta_{i} + \epsilon_{it}$ is the same as this regression: $y_{it} - \bar{y_{l}} = \beta(x_{...

I am very new to the concept of regression. While going through an R output for a multiple regression I came across a set of estimates for the slope and got interested to solve for the same. for 2 ...

An exercise asked to obtain properties of the lineal model $$E[y_i]=\beta x_i\qquad i=1,\cdots,n$$ where $Var[y_i]=\sigma^2$. In one of its sections, we had to calculate and estimator for $\beta$ ...

I understand how to find the coefficients of a bivariate regression and univariate regression w/o an intercept, i.e: Univariate: Y = BX + e ...

everyone! I'm digging in meta-regression and doing hand calculations using WLS to get better understanding of the topic. I'm fine with calculations for univariative model (that is, 1 covariate is ...

I have just started learning Machine Learning and one of the very first topics that I have encountered in this venture is Simple Linear Regression. From Andrew Ng's course, I have learned to perform ...

Does anyone know if there's a general expression for the jth slope coefficient from a multiple regression with K independent variables, in terms of variances and covariances? Obviously, the ...