Slope of a Regression Line vs Coefficient of Determination

The slope $b$ tells you how fast the predicted response rises or falls as the explanatory variable increases by one unit. A positive slope means the line goes up from left to right, and a negative slope means it goes down. For example, in $\hat{y} = 50 + 5x$ the slope 5 predicts 5 more points for each extra hour of study. It is computed as $b = r \cdot \frac{s_y}{s_x}$, where $r$ is the correlation and $s_y$ and $s_x$ are the standard deviations of $y$ and $x$.

The coefficient of determination $r^2$ reports the share of the response's total variation that the least-squares line accounts for, so higher means a better linear fit. It is the square of the correlation coefficient $r$, and multiplying by 100 turns it into a percentage. For example, $r^2 = 0.64$ means 64% of the variation in the response is explained by the linear relationship with the explanatory variable, leaving 36% unexplained. Because it is a square, $r^2$ is never negative and never above 1.