Answer :
### Part A: Creating a Scatterplot
To create the scatterplot, we will use the given data points:
- Birth weight (in pounds): [1.5, 3, 1, 2.5, 0.75]
- Adult weight (in pounds): [10, 17, 8, 14, 5]
You will plot the birth weights on the x-axis and the corresponding adult weights on the y-axis. Here’s the step-by-step process to create the scatterplot:
1. Prepare a Graph Paper or Use a Software Tool:
- Draw two perpendicular lines to form the x-axis (horizontal) and y-axis (vertical).
2. Label Axes:
- Label the x-axis as "Birth Weight (pounds)".
- Label the y-axis as "Adult Weight (pounds)".
3. Choose an Appropriate Scale:
- For the x-axis (Birth Weight), a scale from 0 to 4 pounds would be sufficient.
- For the y-axis (Adult Weight), a scale from 0 to 20 pounds would cover all the data points effectively.
4. Plot the Points:
- Plot the points (1.5, 10), (3, 17), (1, 8), (2.5, 14), and (0.75, 5) on the graph.
5. Mark the Points:
- Mark each of the above points clearly on the graph.
The resulting scatterplot should show a visual representation of how the birth weight of puppies is related to their adult weight.
### Part B: Choosing a Regression Equation
By observing the scatterplot created in Part A, you can analyze the pattern of the data points. Here’s a detailed explanation to help decide which regression model might best fit the data:
1. Linear Regression:
- A linear regression line would be appropriate if the points tend to form a straight line. This suggests a consistent rate of increase in adult weight with an increase in birth weight.
2. Quadratic Regression:
- A quadratic regression (a parabola-like curve) might be a better fit if the relationship between birth weight and adult weight appears to curve. This means the rate of increase in adult weight might slow down for larger birth weights.
3. Exponential Regression:
- An exponential regression model would be suitable if the adult weight increases at an accelerating rate as the birth weight increases.
Analysis Based on Scatterplot:
To decide, visualize the hypothetical scenario where the birth weight is significantly larger, say 10 pounds:
- Linear Relationship: If the relationship is linear, you would expect the adult weight to be proportionately larger, around 50-55 pounds, which might seem unrealistic for small-breed dogs.
- Exponential Growth: If the relationship was exponential, the adult weight would grow very rapidly, which also doesn't align well with the biological limits.
- Quadratic Relationship: If the relationship is quadratic, the adult weight will increase but at a decreasing rate, making a gradual increase more realistic.
Conclusion:
Given the provided data points:
- The points suggest a moderate increase in adult weight as birth weight increases.
- The adult weight does not seem to grow exponentially or change direction sharply.
- Thus, a quadratic regression might be a more suitable model as it allows for the gradual plateauing effect, where the adult weight does not increase indefinitely.
Therefore, although more data would help in refining the choice, a quadratic regression appears to be the best fit for the given data set and the gradual pattern observed in the scatterplot.
To create the scatterplot, we will use the given data points:
- Birth weight (in pounds): [1.5, 3, 1, 2.5, 0.75]
- Adult weight (in pounds): [10, 17, 8, 14, 5]
You will plot the birth weights on the x-axis and the corresponding adult weights on the y-axis. Here’s the step-by-step process to create the scatterplot:
1. Prepare a Graph Paper or Use a Software Tool:
- Draw two perpendicular lines to form the x-axis (horizontal) and y-axis (vertical).
2. Label Axes:
- Label the x-axis as "Birth Weight (pounds)".
- Label the y-axis as "Adult Weight (pounds)".
3. Choose an Appropriate Scale:
- For the x-axis (Birth Weight), a scale from 0 to 4 pounds would be sufficient.
- For the y-axis (Adult Weight), a scale from 0 to 20 pounds would cover all the data points effectively.
4. Plot the Points:
- Plot the points (1.5, 10), (3, 17), (1, 8), (2.5, 14), and (0.75, 5) on the graph.
5. Mark the Points:
- Mark each of the above points clearly on the graph.
The resulting scatterplot should show a visual representation of how the birth weight of puppies is related to their adult weight.
### Part B: Choosing a Regression Equation
By observing the scatterplot created in Part A, you can analyze the pattern of the data points. Here’s a detailed explanation to help decide which regression model might best fit the data:
1. Linear Regression:
- A linear regression line would be appropriate if the points tend to form a straight line. This suggests a consistent rate of increase in adult weight with an increase in birth weight.
2. Quadratic Regression:
- A quadratic regression (a parabola-like curve) might be a better fit if the relationship between birth weight and adult weight appears to curve. This means the rate of increase in adult weight might slow down for larger birth weights.
3. Exponential Regression:
- An exponential regression model would be suitable if the adult weight increases at an accelerating rate as the birth weight increases.
Analysis Based on Scatterplot:
To decide, visualize the hypothetical scenario where the birth weight is significantly larger, say 10 pounds:
- Linear Relationship: If the relationship is linear, you would expect the adult weight to be proportionately larger, around 50-55 pounds, which might seem unrealistic for small-breed dogs.
- Exponential Growth: If the relationship was exponential, the adult weight would grow very rapidly, which also doesn't align well with the biological limits.
- Quadratic Relationship: If the relationship is quadratic, the adult weight will increase but at a decreasing rate, making a gradual increase more realistic.
Conclusion:
Given the provided data points:
- The points suggest a moderate increase in adult weight as birth weight increases.
- The adult weight does not seem to grow exponentially or change direction sharply.
- Thus, a quadratic regression might be a more suitable model as it allows for the gradual plateauing effect, where the adult weight does not increase indefinitely.
Therefore, although more data would help in refining the choice, a quadratic regression appears to be the best fit for the given data set and the gradual pattern observed in the scatterplot.
