Question
A marine biologist studied the relationship between the number of coral reefs, x, in a section of the ocean and the number of fish, y, observed in that area. She modeled the relationship with a scatter plot and used the equation for the regression line. What is the meaning of the slope and the y-intercept of this regression line? Responses The slope means that for every additional coral reef, the number of fish increases by 8. The y-intercept means that when there are no coral reefs, there are 20 fish. The slope means that for every additional coral reef, the number of fish increases by 8. The y-intercept means that when there are no coral reefs, there are 20 fish. The slope means that for every additional coral reef, the number of fish increases by 20. The y-intercept means that when there are 8 coral reefs, there are no fish. The slope means that for every additional coral reef, the number of fish increases by 20. The y-intercept means that when there are 8 coral reefs, there are no fish. The slope means that for every additional fish, there are 8 more coral reefs. The y-intercept means there are no fish when there are no coral reefs. The slope means that for every additional fish, there are 8 more coral reefs. The y-intercept means there are no fish when there are no coral reefs. The slope means that for every 8 additional coral reefs, the number of fish increases by 1. The y-intercept means that the fish population starts at 8.
Answers
GPT-4o mini
To understand the meanings of the slope and the y-intercept in the context of the regression line modeling the relationship between the number of coral reefs (x) and the number of fish (y), we should clarify their interpretations based on standard linear regression concepts.
1. **Slope**: The slope of a regression line represents the change in the dependent variable (number of fish) for each one-unit increase in the independent variable (number of coral reefs). For example, if the slope is 8, this means that for every additional coral reef, the number of fish observed in that area increases by 8.
2. **Y-intercept**: The y-intercept of a regression line represents the value of the dependent variable (number of fish) when the independent variable (number of coral reefs) is equal to zero. If the y-intercept is 20, this means that when there are no coral reefs, there are approximately 20 fish present.
Based on this understanding, the correct response would be:
- The slope means that for every additional coral reef, the number of fish increases by 8. The y-intercept means that when there are no coral reefs, there are 20 fish.
1. **Slope**: The slope of a regression line represents the change in the dependent variable (number of fish) for each one-unit increase in the independent variable (number of coral reefs). For example, if the slope is 8, this means that for every additional coral reef, the number of fish observed in that area increases by 8.
2. **Y-intercept**: The y-intercept of a regression line represents the value of the dependent variable (number of fish) when the independent variable (number of coral reefs) is equal to zero. If the y-intercept is 20, this means that when there are no coral reefs, there are approximately 20 fish present.
Based on this understanding, the correct response would be:
- The slope means that for every additional coral reef, the number of fish increases by 8. The y-intercept means that when there are no coral reefs, there are 20 fish.