Trend lines on scatter plots in Matplotlib - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of scatter plot with linear trend line

What will be the output of this code snippet that plots a scatter plot and adds a linear trend line?

Matplotlib

import matplotlib.pyplot as plt
import numpy as np

x = np.array([1, 2, 3, 4, 5])
y = np.array([2, 4, 5, 4, 5])

plt.scatter(x, y)
coeffs = np.polyfit(x, y, 1)
trend = np.poly1d(coeffs)
plt.plot(x, trend(x), color='red')
plt.show()

A A scatter plot with points at (1,2), (2,4), (3,5), (4,4), (5,5) and a red straight line roughly fitting the points.

B A scatter plot with points and a blue curved line that passes through all points exactly.

C A scatter plot with points but no line is drawn.

D A scatter plot with points and a green horizontal line at y=3.

💡 Hint

Look at how np.polyfit with degree 1 creates a straight line fit.

The code fits a linear (degree 1) polynomial to the points and plots it as a red line. The line approximates the trend of the scatter points.

❓ data_output

intermediate

Number of points above the trend line

Given the following data and trend line, how many points lie above the linear trend line?

Matplotlib

import numpy as np

x = np.array([1, 2, 3, 4, 5])
y = np.array([2, 4, 5, 4, 5])
coeffs = np.polyfit(x, y, 1)
trend = np.poly1d(coeffs)
points_above = sum(y > trend(x))
print(points_above)

A 4

B 3

C 1

D 2

💡 Hint

Compare each y value to the trend line value at the same x.

The trend line values are approximately [2.8, 3.4, 4.0, 4.6, 5.2]. Points with y > trend(x) are at x=2 (4>3.4), x=3 (5>4.0), so 2 points are above.

❓ visualization

advanced

Identify the correct polynomial trend line plot

Which option shows the correct plot of a scatter plot with a quadratic (degree 2) trend line for the data below?

Matplotlib

import matplotlib.pyplot as plt
import numpy as np

x = np.array([1, 2, 3, 4, 5])
y = np.array([1, 4, 9, 16, 25])

plt.scatter(x, y)
coeffs = np.polyfit(x, y, 2)
trend = np.poly1d(coeffs)
plt.plot(x, trend(x), color='green')
plt.show()

A Scatter points forming a perfect square curve with a green curved line passing exactly through all points.

B Scatter points with a green straight line that does not fit the curve well.

C Scatter points with a green curved line that misses all points.

D Scatter points with a green horizontal line at y=10.

💡 Hint

Degree 2 polynomial fits a parabola shape.

The data points are perfect squares, so a quadratic trend line fits exactly and passes through all points.

🔧 Debug

advanced

Identify the error in trend line code

What error will this code raise when trying to plot a trend line on a scatter plot?

Matplotlib

import matplotlib.pyplot as plt
import numpy as np

x = np.array([1, 2, 3, 4, 5])
y = np.array([2, 3, 5, 7, 11])

plt.scatter(x, y)
coeffs = np.polyfit(x, y, 1)
trend = np.poly1d(coeffs)
plt.plot(trend(x), x, color='blue')
plt.show()

A TypeError because plt.plot expects x and y arrays but got reversed.

B No error; the plot shows a blue line but with axes swapped.

C ValueError due to mismatched array lengths in plt.plot.

D SyntaxError due to missing parentheses.

💡 Hint

Check the order of arguments in plt.plot(x, y).

plt.plot(trend(x), x) swaps x and y axes but does not raise an error. The plot will show a line but axes are reversed.

🚀 Application

expert

Calculate and plot residuals from trend line

Given data points and a linear trend line, which code correctly calculates residuals and plots them as a bar chart?

Matplotlib

import matplotlib.pyplot as plt
import numpy as np

x = np.array([1, 2, 3, 4, 5])
y = np.array([2, 3, 5, 7, 11])
coeffs = np.polyfit(x, y, 1)
trend = np.poly1d(coeffs)
residuals = y - trend(x)

plt.bar(x, residuals)
plt.xlabel('x')
plt.ylabel('Residuals')
plt.title('Residuals from Linear Trend Line')
plt.show()

A Calculates residuals as trend(x) - y and plots a line plot instead of bars.

B Calculates residuals as y + trend(x) and plots bars with incorrect values.

C Calculates residuals as y - trend(x) and plots them correctly as bars at each x.

D Calculates residuals as y - trend(x) but plots a scatter plot instead of bars.

💡 Hint

Residuals are actual minus predicted values and bar plot shows magnitude.

Residuals are differences y - predicted y. The code correctly computes and plots them as bars.