To determine the correct answer regarding the equation of the line of best fit and the correlation coefficient \( r \), we need to analyze the provided options.
- Equation Format: The general format for a linear equation is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
- Correlation Coefficient: The correlation coefficient \( r \) ranges from -1 to 1, where values close to 1 (like 0.991) indicate a strong positive correlation, and values closer to 0 indicate no correlation.
Given your options, the most plausible candidates based on high correlation and proper format are:
- Option 1: \( y = 2.964x + 62.286, r = 0.991; \) about 99%
- Option 2: \( y = 2.964x + 62.286, r = 0.991; \) about 89%
- Option 3: \( y = 62.286x + 2.964, r = 0.991; \) about 95%
- Option 4: \( y = 62.286x + 2.964, r = 0.991; \) about 95%
- Option 5: \( y = 3x + 65, r = 0.951; \) about 92%
Analyzing the Options:
- Options 1 and 2 have the same equation, but they differ in the percentage (99% vs. 89%).
- Options 3 and 4 have the equation in the incorrect format (the coefficients and variables are reversed).
- Option 5 offers a different slope and y-intercept with a slightly lower correlation value, indicating a weaker correlation.
Since options 1 and 2 are consistent with each other, and given the correlation coefficient \( r = 0.991 \) is very high, it is likely a strong relationship. Between the two:
- If the correct correlation coefficient is as stated, then Option 1 (with a 99% prediction accuracy) is more reliable than Option 2 (which states 89%).
Conclusion:
The correct response is:
y = 2.964x + 62.286, r = 0.991; about 99%.