The equation of the demand function is \( q=-38.79 p+787.21 \). According to the correlation coefficient, is the demand function a good fit for the data? Since \( |r|<0.8 \), then the regression line is a good fit. since \( |r|>0.8 \), then the regression line is a good fit. Since \( |r|<0.8 \), then the regression line is not a good fit. Since \( |r|>0.8 \), then the regression line is not a good fit.

To determine whether the demand function \( q = -38.79p + 787.21 \) is a good fit for the data based on the correlation coefficient \( r \), we need to analyze the value of \( |r| \). 1. **Understanding the correlation coefficient \( r \)**: - The correlation coefficient \( r \) measures the strength and direction of a linear relationship between two variables. - The value of \( r \) ranges from -1 to 1. - A value of \( |r| < 0.8 \) indicates a weak correlation, while \( |r| > 0.8 \) indicates a strong correlation. 2. **Interpreting the options**: - If \( |r| < 0.8 \), the regression line is considered a good fit for the data. - If \( |r| > 0.8 \), the regression line is considered a good fit for the data. - The statements provided seem to have some inconsistencies regarding the interpretation of \( |r| \). 3. **Conclusion**: - Since the options provided are contradictory, we need to clarify that typically: - If \( |r| > 0.8 \), the regression line is a good fit. - If \( |r| < 0.8 \), the regression line is not a good fit. Given this understanding, the correct interpretation based on the correlation coefficient would be: - If \( |r| < 0.8 \), then the regression line is not a good fit. - If \( |r| > 0.8 \), then the regression line is a good fit. Thus, the correct answer is: - Since \( |r| < 0.8 \), then the regression line is not a good fit.