1. **State the problem:** We are given the regression line equation for IB Diploma points $y$ based on hours spent on social media $x$ for ten female students: $$y = -\frac{2}{3}x + \frac{125}{3}$$ We need to estimate the IB Diploma points for an eleventh girl who spent 34 hours on social media. 2. **Use the regression line formula:** The regression line predicts $y$ (IB points) from $x$ (hours on social media) using: $$y = -\frac{2}{3}x + \frac{125}{3}$$ 3. **Substitute $x=34$ into the equation:** $$y = -\frac{2}{3} \times 34 + \frac{125}{3}$$ 4. **Calculate step-by-step:** $$-\frac{2}{3} \times 34 = -\frac{68}{3}$$ So, $$y = -\frac{68}{3} + \frac{125}{3} = \frac{125 - 68}{3} = \frac{57}{3} = 19$$ 5. **Interpretation:** The estimated IB Diploma points for the eleventh girl is **19 points**. 6. **Reason why this estimate is not reliable:** The original data only included students who spent between 3 and 30 hours on social media. Since 34 hours is outside this range (an extrapolation), the estimate may not be accurate or reliable because the regression line may not hold beyond the observed data range.