Linear Regression in Python (scipy)

Context: FIT1043_MOC · the applied form of linear regression · fit a line with scipy · lab: 30_Projects/FIT1043_Labs/Week5-Regression-Solution.pdf Problem it solves: fit $\hat{y}=a_0+a_{1}x$ to two numeric columns, read the slope/intercept/$r$, and plot the line.

Quick Revision

• 🎯 Trigger: a linear trend between two numeric variables ➔ linregress(x, y) returns slope, intercept, r, p, std_err.
• ⚡ Key Constraint: linregress unpacks five values in order; build predictions with a comprehension slope*xi + intercept.

🔧 Minimal Working Example

from scipy.stats import linregress
import matplotlib.pyplot as plt
 
slope, intercept, r_value, p_value, std_err = linregress(df['Age'], df['Income'])
line = [slope*xi + intercept for xi in df['Age']]     # predicted y for each x
 
plt.scatter(df['Age'], df['Income'])
plt.plot(df['Age'], line, 'r-')
plt.show()

Expected output: the fitted line over the scatter; slope/intercept define it, r_value its correlation strength.

• Fit ➔ slope, intercept, r_value, p_value, std_err = linregress(x, y) (x = independent, y = dependent).
• Predict / draw ➔ line = [slope*xi + intercept for xi in x], then plt.plot(x, line).
• Read $r$ ➔ r_value is Pearson correlation ($-\mathrm{1..1}$); its sign matches the slope’s (e.g. Age↑ vs Runs↓ gives negative slope and $r$).

🔀 Variations

• Report the fit ➔ print('slope %f intercept %f' % (slope, intercept)); print('r %f' % r_value).
• Predict one point ➔ slope*70 + intercept — but only trust it where the relationship is actually linear.

✍️ Practice

Practice 1: Fit Age → Runs for a players DataFrame, print the slope and r-value, and plot the line over the data.

Reference solution

slope, intercept, r_value, p_value, std_err = linregress(df['Age'], df['Runs'])
print('slope: %f  r: %f' % (slope, r_value))
line = [slope*xi + intercept for xi in df['Age']]
plt.plot(df['Age'], line, 'r-'); plt.scatter(df['Age'], df['Runs']); plt.show()

• Key move: unpack all five returns; the comprehension turns slope/intercept into a plottable line.

⚠️ Common Mistakes

• 💡 Don’t extrapolate past the linear range ➔ a model fit on ages 18–40 can’t predict income at 70 if the true relation bends — linear regression assumes linearity.
• 💡 Order of returns matters ➔ linregress gives (slope, intercept, r, p, std_err); mis-unpacking silently mislabels them.