To solve this, we need to use the fact that the coefficient of determination $r^2$ is given as 0.7783. The relationship between the correlation coefficient $r$ and $r^2$ is as follows:

$r = \pm \sqrt{r^2}$

Thus, we can calculate $r$:

$r = \sqrt{0.7783} \approx 0.882$

Interpretation of Statements:

1. "About 78% of the variation in ticket price can be explained by the distance flown."

   • This is correct because $r^2 = 0.7783$, which means 77.83% of the variation in ticket price is explained by the distance flown.

2. "The correlation coefficient, r, is 0.882."

   • This is correct because $r = \sqrt{0.7783} \approx 0.882$.

3. "About 78% of the variation in distance flown can be explained by the ticket price."

   • This statement is false. $r^2$ here refers to the percentage of variation in ticket price explained by the distance flown, not the other way around.

4. "The correlation coefficient, r, is 0.606."

   • This is false. The correlation coefficient is 0.882, not 0.606.

5. "About 22% of the variation in ticket price can be explained by the distance flown."

   • This is false. $100\% - 77.83\% = 22.17\%$, so 22% of the variation in ticket price cannot be explained by the distance flown.

6. "About 88% of the variation in ticket price can be explained by the distance flown."

   • This is false because 77.83% of the variation in ticket price can be explained, not 88%.

Conclusion:

The true set of statements is:

• "About 78% of the variation in ticket price can be explained by the distance flown."
• "The correlation coefficient, r, is 0.882."

Would you like further details or have any other questions?

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Here are some related questions to consider:

1. How is the $r^2$ value interpreted in linear regression?
2. What is the difference between $r$ and $r^2$ in correlation analysis?
3. How would the value of $r$ change if the variables were inversely related?
4. Can $r^2$ be negative in any scenario?
5. How do outliers affect the correlation coefficient $r$?

Tip: The closer the correlation coefficient $r$ is to 1 or -1, the stronger the linear relationship between the two variables.