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Linear Modelingmedium
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The standard error of the predicted mean response at x0x_0x0​ is given by SE(μ^Y∣x0)=se1n+(x0−xˉ)2∑(xi−xˉ)2SE(\hat{\mu}_{Y|x_0}) = s_e \sqrt{\frac{1}{n} + \frac{(x_0 - \bar{x})^2}{\sum (x_i - \bar{x})^2}}SE(μ^​Y∣x0​​)=se​n1​+∑(xi​−xˉ)2(x0​−xˉ)2​​. At what value of x0x_0x0​ is the width of the confidence interval for the mean response minimized?