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Linear Modelinghard
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A researcher fits a simple linear regression model Y=β0+β1X+ϵY = \beta_0 + \beta_1 X + \epsilonY=β0​+β1​X+ϵ to n=20n = 20n=20 data points. Given that the total sum of squares SST=500SST = 500SST=500, the sum of squared errors SSE=125SSE = 125SSE=125, and the sum of squares of the independent variable ∑(Xi−Xˉ)2=80\sum (X_i - \bar{X})^2 = 80∑(Xi​−Xˉ)2=80, what is the variance of the OLS slope estimator Var(β^1)Var(\hat{\beta}_1)Var(β^​1​)?