WHEN CONSTRUCTING AN EQUATION OF A LINEAR SMOOTHING FUNCTION hat (y)=alpha _(0)+alpha _(1)x BY THE METHOD OF LEAST SQUARES USING THE FORMULA =(1)/(n)sum _(i=1)^nx_(i)y_(i) . THE FOLLOWING PARAMETER IS DETERMINED Select one: overline (xy) y^2 bar (y) bar (x) x^2

The correct answer is $\overline{xy}$.<br /><br />In the formula for the least squares method, the parameter $\alpha_1$ is determined by the formula:<br /><br />$\alpha_1 = \frac{1}{n}\sum_{i=1}^{n}x_iy_i - \overline{x}\overline{y}$<br /><br />where $x_i$ and $y_i$ are the values of the independent variable and the dependent variable, respectively, and $n$ is the number of data points.<br /><br />The term $\overline{xy}$ represents the average product of the independent variable and the dependent variable, which is used to calculate the slope of the linear smoothing function.<br /><br />The other options, $y^2$, $\bar{y}$, $\bar{x}$, and $x^2$, are not the correct parameters for determining the slope of the linear smoothing function using the least squares method.