Let's address this problem step by step.
1. Understanding the Problem:
- We have a table with daily temperatures and the corresponding number of cakes sold.
- We are required to determine if there's a relationship between daily temperature and cakes sold and, if there is, describe the nature of that relationship.
2. Data Given:
- Daily Temperatures: [42, 45, 48, 64, 62, 64, 67, 75, 84]
- Cakes Sold: [39, 52, 31, 61, 72, 35, 61, 34, 58]
3. Calculating the Correlation Coefficient:
- The correlation coefficient measures the strength and direction of a linear relationship between two variables.
- The correlation coefficient, denoted by [tex]\( r \)[/tex], ranges from -1 to 1.
- [tex]\( r = 1 \)[/tex] means a perfect positive linear relationship.
- [tex]\( r = -1 \)[/tex] means a perfect negative linear relationship.
- [tex]\( r = 0 \)[/tex] means no linear relationship.
4. Result Interpretation:
- The computed correlation coefficient is approximately [tex]\( 0.28 \)[/tex].
- This value indicates a weak positive linear relationship between daily temperature and the number of cakes sold, since [tex]\( 0.28 \)[/tex] is closer to 0 than to 1.
5. Conclusion:
- Based on this weak positive correlation coefficient of [tex]\( 0.28 \)[/tex], we can conclude that Amelle's cake sales are positively affected by the daily temperature, albeit weakly.
So, the completed statement based on our results would be:
The correlation coefficient is close to 0.28. Based on this information, we can conclude that Amelle's cake sales are positively affected by the daily temperature.
