1. The problem is to analyze the relationship between height and weight from the given data points. 2. We can use linear regression to find the best fit line, which has the formula $$y = mx + b$$ where $y$ is weight, $x$ is height, $m$ is the slope, and $b$ is the y-intercept. 3. To find $m$ and $b$, we use the formulas: $$m = \frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2}$$ $$b = \frac{\sum y - m \sum x}{n}$$ where $n$ is the number of data points. 4. Calculate sums: $$\sum x = 71+72+73+70+72+72+70+74+78+71+74+73+76+77+76+77+73+76+76+70+75+71+77+75+75 = 1823$$ $$\sum y = 186+211+220+165+180+195+175+202+240+170+180+185+257+215+287+220+200+223+200+220+215+195+194+195+225 = 5165$$ $$\sum x^2 = 71^2+72^2+73^2+70^2+72^2+72^2+70^2+74^2+78^2+71^2+74^2+73^2+76^2+77^2+76^2+77^2+73^2+76^2+76^2+70^2+75^2+71^2+77^2+75^2+75^2 = 13295$$ $$\sum xy = 71\times186 + 72\times211 + 73\times220 + 70\times165 + 72\times180 + 72\times195 + 70\times175 + 74\times202 + 78\times240 + 71\times170 + 74\times180 + 73\times185 + 76\times257 + 77\times215 + 76\times287 + 77\times220 + 73\times200 + 76\times223 + 76\times200 + 70\times220 + 75\times215 + 71\times195 + 77\times194 + 75\times195 + 75\times225 = 377,095$$ 5. Number of points $n=25$. 6. Calculate slope $m$: $$m = \frac{25 \times 377095 - 1823 \times 5165}{25 \times 13295 - 1823^2} = \frac{9427375 - 9418795}{332375 - 3323329} = \frac{8580}{1046} \approx 8.2$$ 7. Calculate intercept $b$: $$b = \frac{5165 - 8.2 \times 1823}{25} = \frac{5165 - 14948.6}{25} = \frac{-9783.6}{25} = -391.34$$ 8. The regression line is: $$y = 8.2x - 391.34$$ 9. This means for each additional inch in height, weight increases by about 8.2 units on average.