A health clinic records the heights, in centimetres, and masses, in kilograms, of six teenagers…

Step 1. The correlation. The mean height is $\dfrac{998}{6} = 166.33$ and the mean mass is $60$. The sums give $r = 0.988$.

Step 2. The slope. $b = \dfrac{S_{xy}}{S_{xx}} = 0.817\ \text{kg per cm}$.

Step 3. The new units. Heights in metres are $\dfrac{1}{100}$ of the old numbers and masses in grams are $1000$ times the old numbers. A change in height of $1$ metre is $100$ centimetres, which goes with $100 \times 0.817\ \text{kg} = 81.7\ \text{kg} = 81700\ \text{g}$. So the slope is $81723\ \text{g per m}$ with the unrounded value.

Step 4. What happens to $r$. Both changes multiply by positive numbers, so $r$ stays $0.988$.