1. **Stating the problem:** We have data on the number of gender equality training sessions attended ($x$) and the corresponding gender equality attitude scores ($y$) for six employees. We want to present a scatter plot, compute the correlation coefficient $r$, and find the regression line equation. 2. **Data points:** $$ (1,68), (2,71), (2,70), (3,75), (4,77), (5,80) $$ 3. **Formula for correlation coefficient $r$:** $$ r = \frac{n\sum xy - \sum x \sum y}{\sqrt{(n\sum x^2 - (\sum x)^2)(n\sum y^2 - (\sum y)^2)}} $$ where $n$ is the number of data points. 4. **Calculate sums:** $$ \sum x = 1+2+2+3+4+5 = 17 $$ $$ \sum y = 68+71+70+75+77+80 = 441 $$ $$ \sum xy = (1)(68)+(2)(71)+(2)(70)+(3)(75)+(4)(77)+(5)(80) = 68+142+140+225+308+400 = 1283 $$ $$ \sum x^2 = 1^2+2^2+2^2+3^2+4^2+5^2 = 1+4+4+9+16+25 = 59 $$ $$ \sum y^2 = 68^2+71^2+70^2+75^2+77^2+80^2 = 4624+5041+4900+5625+5929+6400 = 32519 $$ 5. **Calculate numerator and denominator for $r$:** $$ n\sum xy - \sum x \sum y = 6(1283) - 17(441) = 7698 - 7497 = 201 $$ $$ \sqrt{(n\sum x^2 - (\sum x)^2)(n\sum y^2 - (\sum y)^2)} = \sqrt{6(59) - 17^2} \times \sqrt{6(32519) - 441^2} $$ Calculate each part: $$ 6(59) - 289 = 354 - 289 = 65 $$ $$ 6(32519) - 194481 = 195114 - 194481 = 633 $$ So denominator: $$ \sqrt{65 \times 633} = \sqrt{41145} \approx 202.85 $$ 6. **Correlation coefficient:** $$ r = \frac{201}{202.85} \approx 0.991 $$ This indicates a very strong positive linear relationship. 7. **Equation of regression line:** The regression line is: $$ y = a + bx $$ where $$ b = \frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2} = \frac{201}{65} \approx 3.092 $$ $$ a = \bar{y} - b\bar{x} = \frac{441}{6} - 3.092 \times \frac{17}{6} = 73.5 - 3.092 \times 2.833 = 73.5 - 8.76 = 64.74 $$ 8. **Final regression line:** $$ y = 64.74 + 3.092x $$ This means for each additional training session attended, the equality score increases by about 3.092 points on average.