Koala Speeds Problem¶
You believe there's a linear relationship between the weight of an adult koala and how fast it runs. You gather some data.
import numpy as np # Create a random number generator rng = np.random.default_rng(4321) # (1)! # Make data weights = rng.uniform(low=10, high=20, size=35) speeds = -0.08* weights + 7.2 + rng.normal(loc=0, scale=0.5, size=len(weights)) ages = rng.uniform(low=3, high=18, size=len(weights)) print(weights) # [10.03 18.08 15.33 ... 17.07 13.32 10.08] print(speeds) # [6.33 5.55 6.33 ... 5.48 6.41 6.55] print(ages) # [12.51 11.16 10.36 ... 17.24 16.06 7.89]
You fit a linear regression model to this data,
y = mx + b, with slope
m = -0.15 and offset
b = 8.2.
- Make a scatter plot of speed (y) vs weight (x), varying the size of each point by the koala's age.
- Overlay the linear regression line defined by
- Include the linear regression equation inside the Axes, near the top right. (Make the position of the equation independent of the data!)
Show the plot