Trend lines on scatter plots in Matplotlib - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to plot a scatter plot using matplotlib.

Matplotlib

import matplotlib.pyplot as plt

x = [1, 2, 3, 4, 5]
y = [2, 3, 5, 7, 11]

plt.[1](x, y)
plt.show()

Drag options to blanks, or click blank then click option'

Ascatter

Bplot

Cbar

Dhist

Attempts:

3 left

💡 Hint

Common Mistakes

Using plt.plot instead of plt.scatter for scatter plots.

Using plt.bar which is for bar charts.

The scatter function creates a scatter plot, which is used to show points on a graph.

2fill in blank

medium

Complete the code to calculate the slope and intercept of a linear trend line using numpy.

Matplotlib

import numpy as np

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

slope, intercept = np.polyfit(x, y, [1])

Drag options to blanks, or click blank then click option'

A0

B2

C3

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using 2 or higher degree which fits curves, not lines.

Using 0 which is a constant.

The degree of the polynomial for a linear fit is 1.

3fill in blank

hard

Fix the error in the code to plot the trend line on the 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])

slope, intercept = np.polyfit(x, y, 1)

plt.scatter(x, y)
plt.plot(x, slope * [1] + intercept, color='red')
plt.show()

Drag options to blanks, or click blank then click option'

Ay

Bx

Cslope

Dintercept

Attempts:

3 left

💡 Hint

Common Mistakes

Using y instead of x in the line equation.

Using slope or intercept alone without x.

The trend line is calculated as slope times x plus intercept, so x must be used in the plot.

4fill in blank

hard

Fill both blanks to create a dictionary of squared values for numbers greater than 3.

Matplotlib

numbers = [1, 2, 3, 4, 5]
squares = {num: num[1]2 for num in numbers if num [2] 3}

Drag options to blanks, or click blank then click option'

A**

B>

C<

D*

Attempts:

3 left

💡 Hint

Common Mistakes

Using * instead of ** for power.

Using < instead of > in the condition.

Use ** for exponentiation and > to filter numbers greater than 3.

5fill in blank

hard

Fill all three blanks to create a dictionary of uppercase keys and values greater than 0.

Matplotlib

data = {'a': 1, 'b': -2, 'c': 3}
result = [1]: [2] for [3], [2] in data.items() if [2] > 0

Drag options to blanks, or click blank then click option'

Ak.upper()

Bv

Ck

Ditem

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'item' as loop variable without unpacking.

Not converting keys to uppercase.

Keys are converted to uppercase with k.upper(), values are v, and the loop variable is k and v unpacked from data.items().

Practice

1. What is the main purpose of adding a trend line to a scatter plot in matplotlib?

easy

A. To show the overall pattern or relationship between variables

B. To add colors to the scatter points

C. To change the size of scatter points

D. To remove outliers from the data

Solution

1. Step 1: Understand scatter plot purpose

   A scatter plot shows individual data points but may not clearly show the overall trend.

2. Step 2: Role of trend line

   A trend line summarizes the general direction or pattern in the data, making relationships easier to see.

3. Final Answer:

   To show the overall pattern or relationship between variables -> Option A

4. Quick Check:

   Trend line = overall pattern [OK]

Hint: Trend lines summarize data direction, not point details [OK]

Common Mistakes:

• Thinking trend lines change point colors
• Confusing trend lines with point size changes
• Believing trend lines remove data points

2. Which of the following code snippets correctly fits a linear trend line to data arrays x and y using numpy?

easy

A. coefficients = np.polyfit(x, y, 1)

B. coefficients = np.polyfit(y, x, 1)

C. coefficients = np.polyfit(x, y, 2)

D. coefficients = np.polyfit(x, y)

Solution

1. Step 1: Understand np.polyfit parameters

   np.polyfit(x, y, degree) fits a polynomial of given degree to x and y data.

2. Step 2: Correct usage for linear fit

   For a linear trend line, degree = 1, and x is independent variable, y is dependent variable.

3. Final Answer:

   coefficients = np.polyfit(x, y, 1) -> Option A

4. Quick Check:

   np.polyfit(x, y, 1) fits linear trend [OK]

Hint: Use degree=1 for linear trend with np.polyfit(x, y, 1) [OK]

Common Mistakes:

• Swapping x and y in np.polyfit
• Omitting degree parameter
• Using degree 2 for linear trend

3. Given the code below, what will be the output of print(trendline(3))?

import numpy as np
x = np.array([1, 2, 3, 4])
y = np.array([2, 4, 6, 8])
coefficients = np.polyfit(x, y, 1)
trendline = np.poly1d(coefficients)
print(trendline(3))

medium

A. Error due to incorrect polyfit usage

B. 5.0

C. 9.0

D. 6.0

Solution

1. Step 1: Analyze data and polyfit

   Data y doubles x (2,4,6,8), so linear fit slope ~2 and intercept ~0.

2. Step 2: Calculate trendline at x=3

   trendline(3) = 2*3 + 0 = 6.0

3. Final Answer:

   6.0 -> Option D

4. Quick Check:

   trendline(3) = 6.0 [OK]

Hint: Check if y is roughly 2*x; then trendline(3) = 6 [OK]

Common Mistakes:

• Confusing x and y order in polyfit
• Forgetting poly1d creates function
• Assuming error instead of numeric output

4. Identify the error in the following code that tries to plot a scatter plot with a trend line:

import numpy as np
import matplotlib.pyplot as plt
x = np.array([1, 2, 3, 4])
y = np.array([2, 3, 5, 7])
coeff = np.polyfit(x, y, 1)
trend = np.poly1d(coeff)
plt.scatter(x, y)
plt.plot(x, trend)
plt.show()

medium

A. np.polyfit arguments are in wrong order

B. plt.plot(x, trend) should be plt.plot(x, trend(x))

C. plt.scatter should be called after plt.plot

D. Missing plt.xlabel and plt.ylabel calls

Solution

1. Step 1: Check trend line plotting

   plt.plot expects y-values, but trend is a function, not values.

2. Step 2: Correct function call

   Call trend(x) to get y-values for plotting: plt.plot(x, trend(x))

3. Final Answer:

   plt.plot(x, trend) should be plt.plot(x, trend(x)) -> Option B

4. Quick Check:

   Plot function needs y-values, not function [OK]

Hint: Call trend(x) to get y-values for plt.plot [OK]

Common Mistakes:

• Passing function instead of values to plt.plot
• Swapping x and y in polyfit
• Thinking plot order affects output
• Missing axis labels is not an error

5. You have noisy data with outliers. Which approach best improves the trend line fit on a scatter plot using matplotlib and numpy?

hard

A. Plot scatter without trend line to avoid confusion

B. Use np.polyfit with degree 1 on all data points

C. Remove outliers before fitting trend line with np.polyfit

D. Use plt.plot instead of plt.scatter for all points

Solution

1. Step 1: Understand effect of outliers

   Outliers can distort the trend line fit, making it less representative.

2. Step 2: Improve fit by removing outliers

   Removing or filtering outliers before fitting helps get a better trend line.

3. Final Answer:

   Remove outliers before fitting trend line with np.polyfit -> Option C

4. Quick Check:

   Remove outliers for better trend line [OK]

Hint: Filter outliers before fitting trend line for accuracy [OK]

Common Mistakes:

• Fitting trend line on all data including outliers
• Skipping trend line when data is noisy
• Confusing plot types for trend line fitting