The problem in the image states:

• "If the line of regression of $Y$ on $X$ is $Y = 9X + 5$, then the estimated value of $Y$ when $X = 2$ is 18."

To solve this, we will substitute $X = 2$ into the regression equation $Y = 9X + 5$:

$Y = 9(2) + 5 = 18 + 5 = 23$

Thus, the estimated value of $Y$ when $X = 2$ is 23, not 18. This suggests that there might be an error in the statement.

Would you like further clarification on this or any additional details?

Here are five related questions for further exploration:

1. How is a line of regression derived from data?
2. What is the difference between regression of $Y$ on $X$ and regression of $X$ on $Y$?
3. How would changing the slope or intercept affect the regression line?
4. How does one calculate residuals for regression lines?
5. What are the assumptions behind linear regression?

Tip: Always check for the accuracy of estimated values by substituting directly into the regression equation!