From the given data estimate the slope of the regression line by the least squares method in order to compute coefficient of determination.

The least squares estimate of the $\textbf{slope}$ is

$$\begin{align*} b_1 = \hat{\beta}_1 = \dfrac{\sum (x_i - \overline{x})(y_i - \overline{y})}{\sum \left(x_i - \overline{x}\right)^2} = \frac{S_{xy}}{S_{xx}} \end{align*}$$

where $S_{xy}$ can be computed using formula

$$\begin{align*} S_{xy} = \sum x_i y_i - \frac{1}{n} \left( \sum x_i \right) \left( \sum y_i \right), \end{align*}$$

and $S_{xx}$ can be computed using formula

$$\begin{align*} S_{xx} = \sum x_i^2 - \frac{1}{n} \left( \sum x_i \right)^2. \end{align*}$$

The least squares estimate of the $\textbf{intercept}$ is

$$\begin{align*} b_0 = \hat{\beta}_0 = \dfrac{\sum y_i - \hat{\beta}_1 \sum x_i}{n} = \overline{y} - \hat{\beta}_1 \overline{x}. \end{align*}$$