1. The regression equation is given by $$\hat{y} = b_0 + b_1 x$$ where $$b_0$$ is the y-intercept and $$b_1 = 0.5$$ is the slope. 2. The slope $$b_1 = 0.5$$ means that for every increase of 1 unit in $$x$$, the predicted $$y$$ (\(\hat{y}\)) increases by 0.5 units. 3. Checking Option A: For every 0.05 increase in $$x$$, increase in $$\hat{y}$$ is $$0.5 \times 0.05 = 0.025$$, not 0.05, so Option A is incorrect. 4. Checking Option B: For every 10 unit increase in $$x$$, increase in $$\hat{y}$$ is $$0.5 \times 10 = 5$$, which matches Option B. 5. Checking Option C: It says $$\hat{y}$$ decreases by 5 for a 10 increase in $$x$$, which contradicts the positive slope, so Option C is incorrect. 6. Checking Option D: For a 0.05 increase in $$x$$, it states $$\hat{y}$$ increases by 1, but actually it's $$0.025$$ as computed above, so Option D is incorrect. **Final answer:** Option B is correct because the slope tells us $$\hat{y}$$ increases by 0.5 for each 1 unit increase of $$x$$, so for 10 units, it increases by 5.