To interpret the slope and y-intercept of the linear model representing the average weight of dogs by age in months, we need to establish what each component means in the context of the data.
Given Information:
- The ordered pair provided is (9, 42), which means that at 9 months of age, the average weight of the dogs is 42 pounds.
- We need to calculate and interpret the slope as well as the y-intercept.
Slope Interpretation:
-
Slope Calculation: From the data provided, weight decreases as age increases. To determine the slope \( m \), we'll consider how weight changes with respect to time.
Assuming you have two points for calculation, let's say you use points around the ordered pair (9, 42). For the sake of this example, if we consider an estimated slope based on the linear relationship from the data:
- Suppose we use (8, 44) and (10, 40) as data points around (9, 42).
- The slope \( m \) can be calculated as follows:
\[ m = \frac{(40 - 44)}{(10 - 8)} = \frac{-4}{2} = -2 \]
Thus the slope is -2 pounds per month, indicating that with each additional month, the average weight of the dogs decreases by approximately 2 pounds.
-
Slope Interpretation: The slope of -2 means that on average, for every additional month of age, the average weight of the dogs decreases by 2 pounds.
Y-Intercept Interpretation:
-
Y-Intercept Definition: The y-intercept is the value of the dependent variable (average weight) when the independent variable (age) is zero. In this case, the y-intercept is (0, 0), which indicates that at 0 months of age (birth), the average weight of the dog is 0 pounds.
-
Y-Intercept Interpretation: The y-intercept suggests that when the dogs are newly born, they start at a weight of 0 pounds. This is a theoretical value because, in real life, newborn puppies do have some weight, but scientifically, it helps us understand that prior to birth, the average weight is categorized as zero.
Conclusion:
- Slope: -2 pounds/month (indicating weight decreases as dogs age).
- Y-Intercept: At 0 months, the average weight is 0 pounds (theoretical starting point).
Please note that the actual values should be computed from the provided data points in your dataset for precise calculations.