FORMULA FOR CALCULATING THE AVERAGE bar (x) IN THE EQUATION OF THE LINEAR SMOOTHING FUNCTION hat (y)=alpha _(0)+alpha _(1)x BY THE METHOD OF LEAST SQUARES Select one: =(1)/(n)sum _(i=1)^nx_(i)^2 =sum _(i=1)^nx_(i) =(1)/(n)sum _(i=1)^nx_(i)y_(i) =(1)/(n)sum _(i=1)^ny_(i) D =(1)/(n)sum _(i=1)^nx_(i)

The correct answer is1}{n}\sum _{i=1}^{n}x_{i}$<br /><br />Explanation:<br />In the equation of the linear smoothing function $\hat {y}=\alpha _{0}+\alpha _{1}x$, the average $\bar {x}$ is calculated as the mean of the values of $x$. The formula for calculating the average $\bar {x}$ is $\frac {1}{n}\sum _{i=1}^{n}x_{i}$, where $n$ is the number of data points and $x_{i}$ represents the values of $x$.