t the multivariate OLS formula, $\hat{\beta}^{O L S}=\left(\mathbf{X}^{\prime} \mathbf{X}\right)^{-\mathbf{1}} \mathbf{X}^{\prime} \mathbf{y}$ prod first row is $\hat{\beta}_{0}^{O L S}$ and whose second row is $\hat{\beta}_{1}^{O L S}$ from part

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∻Solution by Steps∻ ‖ step 1 ⋮ To understand the multivariate OLS formula, we recognize that it is used to estimate the coefficients $ \hat{\beta}^{OLS} $ in a linear regression model. The formula is given by $ \hat{\beta}^{OLS} = (\mathbf{X}'\mathbf{X})^{-1}\mathbf{X}'\mathbf{y} $, where $ \mathbf{X} $ is the matrix of explanatory variables, $ \mathbf{y} $ is the vector of the dependent variable, and $ \mathbf{X}' $ is the transpose of $ \mathbf{X} $. ‖ ‖ step 2 ⋮ To find $ \hat{\beta}_{0}^{OLS} $ and $ \hat{\beta}_{1}^{OLS} $, we need to compute the product $ (\mathbf{X}'\mathbf{X})^{-1}\mathbf{X}'\mathbf{y} $ and extract the first and second rows of the resulting vector. ‖ ‖ step 3 ⋮ Assuming the matrix multiplication and inversion have been correctly computed, $ \hat{\beta}_{0}^{OLS} $ is the first element of the vector $ \hat{\beta}^{OLS} $, and $ \hat{\beta}_{1}^{OLS} $ is the second element of this vector. ‖ ∻Answer∻ ⚹ The first row of the vector $ \hat{\beta}^{OLS} $ is $ \hat{\beta}_{0}^{OLS} $ and the second row is $ \hat{\beta}_{1}^{OLS} $. ⚹ ∻Key Concept∻ ⚹Estimation of regression coefficients in OLS⚹ ∻Explanation∻ ⚹The OLS formula is used to estimate the coefficients of a linear regression model, where $ \hat{\beta}_{0}^{OLS} $ represents the intercept and $ \hat{\beta}_{1}^{OLS} $ represents the slope coefficient associated with the first explanatory variable.⚹◊What is the interpretation of the coefficient $\hat{\beta}_1^{OLS}$ in the multivariate OLS formula?⍭ Generate me a similar question◊

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