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5. The formula for the ordinary least squares slope parameter in a simple linear regression model Suppose the simple linear regression model is given as $y = \beta_0 + \beta_1x + u$. Assuming $\sum_{i=1}^{n} (x_i - \bar{x})^2 > 0$, which of the following best represents the ordinary least squares (OLS) slope parameter $\hat{\beta_1}$? Where: $\hat{\rho}_{xy}$ = the sample covariance between $x_i$ and $y_i$. $\hat{\sigma}_{x}$ = the sample standard deviation of $x_i$ $\hat{\sigma}_{y}$ = the sample standard deviation of $y_i$ $\circ \frac{\hat{\rho}_{xy}}{\left(\frac{\hat{\sigma}_x}{\hat{\sigma}_y}\right)}$ $\circ \frac{\hat{\rho}_{xy}}{\left(\frac{\hat{\sigma}_y}{\hat{\sigma}_x}\right)}$ $\circ \frac{\hat{\rho}_{xy}}{\left(\hat{\sigma}_x \hat{\sigma}_y\right)}$ $\circ \hat{\rho}_{xy} \left(\frac{\hat{\sigma}_x}{\hat{\sigma}_y}\right)$ <0 >0 Suppose you collect data and $x_i$ and $y_i$ are positively correlated in your sample. You know that after using OLS to estimate the simple linear regression model, $\hat{\beta_1}$ must be

          5. The formula for the ordinary least squares slope parameter in a simple linear regression model
Suppose the simple linear regression model is given as $y = \beta_0 + \beta_1x + u$. Assuming $\sum_{i=1}^{n} (x_i - \bar{x})^2 > 0$, which of the following best represents the
ordinary least squares (OLS) slope parameter $\hat{\beta_1}$?
Where:
$\hat{\rho}_{xy}$ = the sample covariance between $x_i$ and $y_i$.
$\hat{\sigma}_{x}$ = the sample standard deviation of $x_i$
$\hat{\sigma}_{y}$ = the sample standard deviation of $y_i$
$\circ \frac{\hat{\rho}_{xy}}{\left(\frac{\hat{\sigma}_x}{\hat{\sigma}_y}\right)}$
$\circ \frac{\hat{\rho}_{xy}}{\left(\frac{\hat{\sigma}_y}{\hat{\sigma}_x}\right)}$
$\circ \frac{\hat{\rho}_{xy}}{\left(\hat{\sigma}_x \hat{\sigma}_y\right)}$
$\circ \hat{\rho}_{xy} \left(\frac{\hat{\sigma}_x}{\hat{\sigma}_y}\right)$
<0
>0
Suppose you collect data and $x_i$ and $y_i$ are positively correlated in your sample. You know that after using OLS to estimate the simple linear
regression model, $\hat{\beta_1}$ must be

5. The formula for the ordinary least squares slope parameter in a simple linear regression model
Suppose the simple linear regression model is given as y = β0 + β1x + u. Assuming ∑i=1^n (xi - x̅)^2 > 0, which of the following best represents the
ordinary least squares (OLS) slope parameter β̂1̂?
Where:
ρ̂xy = the sample covariance between xi and yi.
σ̂x = the sample standard deviation of xi
σ̂y = the sample standard deviation of yi
∘(ρ̂xy)/(((σ̂x)/(σ̂y)))
∘(ρ̂xy)/(((σ̂y)/(σ̂x)))
∘(ρ̂xy)/((σ̂x σ̂y))
∘ρ̂xy((σ̂x)/(σ̂y))
<0
>0
Suppose you collect data and xi and yi are positively correlated in your sample. You know that after using OLS to estimate the simple linear
regression model, β̂1̂ must be

Added by Dennis D.

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