Question
Data from Previous Truck Head Gaskets
Temperature (°C) Damage Index
12 11
13 8
14 8
16 2
18 2
19 2
19 2
19 1
19 1
20 0
21 4
21 0
21 0
Scientists believe there is a link between ambient temperature and damage to a head gasket on a car. Using the provided information draw a scatterplot of the data.
Describe the correlation for temperatures less than 20° Celsius
Responses
A There is no correlation.There is no correlation.
B There is a nonlinear correlation.There is a nonlinear correlation.
C There is a weak negative correlation.There is a weak negative correlation.
D There is a strong positive correlation.There is a strong positive correlation.
E There is a strong negative correlation.
Temperature (°C) Damage Index
12 11
13 8
14 8
16 2
18 2
19 2
19 2
19 1
19 1
20 0
21 4
21 0
21 0
Scientists believe there is a link between ambient temperature and damage to a head gasket on a car. Using the provided information draw a scatterplot of the data.
Describe the correlation for temperatures less than 20° Celsius
Responses
A There is no correlation.There is no correlation.
B There is a nonlinear correlation.There is a nonlinear correlation.
C There is a weak negative correlation.There is a weak negative correlation.
D There is a strong positive correlation.There is a strong positive correlation.
E There is a strong negative correlation.
Answers
Answered by
GPT-4o mini
To draw a scatterplot, you would typically plot the Temperature (°C) on the x-axis and the Damage Index on the y-axis. However, since I cannot generate visual plots directly, I can guide you through how to interpret the data and analyze the correlation.
Looking at the provided data for temperatures less than 20°C, we have the following points:
- (12, 11)
- (13, 8)
- (14, 8)
- (16, 2)
- (18, 2)
- (19, 2)
- (19, 2)
- (19, 1)
- (19, 1)
When you plot these points:
- You will notice that as the temperature increases from 12°C to 19°C, the Damage Index appears to decrease.
- Specifically, the values go from 11 to 8, then stay at 8, drop to 2 and subsequently stay low at 2, 2, 1, etc.
This indicates that there is a trend where increased temperature correlates with a decrease in damage until temperature stabilizes around 19°C.
### Correlation Analysis:
Given that the Damage Index is decreasing as the temperature rises up to 19°C, we can conclude that there is a correlation.
- Since the relationship is not perfectly linear and there’s variability in the damage index values as temperatures approach 19°C, the correlation might not fit a strong linear model.
### Conclusion:
For temperatures less than 20°C, the most fitting description from the options given would be:
**C. There is a weak negative correlation.**
This choice reflects that as the temperature rises, the Damage Index tends to decrease, albeit not in a perfectly linear fashion as it stabilizes at lower values.
Looking at the provided data for temperatures less than 20°C, we have the following points:
- (12, 11)
- (13, 8)
- (14, 8)
- (16, 2)
- (18, 2)
- (19, 2)
- (19, 2)
- (19, 1)
- (19, 1)
When you plot these points:
- You will notice that as the temperature increases from 12°C to 19°C, the Damage Index appears to decrease.
- Specifically, the values go from 11 to 8, then stay at 8, drop to 2 and subsequently stay low at 2, 2, 1, etc.
This indicates that there is a trend where increased temperature correlates with a decrease in damage until temperature stabilizes around 19°C.
### Correlation Analysis:
Given that the Damage Index is decreasing as the temperature rises up to 19°C, we can conclude that there is a correlation.
- Since the relationship is not perfectly linear and there’s variability in the damage index values as temperatures approach 19°C, the correlation might not fit a strong linear model.
### Conclusion:
For temperatures less than 20°C, the most fitting description from the options given would be:
**C. There is a weak negative correlation.**
This choice reflects that as the temperature rises, the Damage Index tends to decrease, albeit not in a perfectly linear fashion as it stabilizes at lower values.