Linear regression with np.polyfit() in NumPy - Mini Project: Build & Apply

Linear regression with np.polyfit()

📖 Scenario: You are a data analyst at a small store. You want to understand how the number of hours spent advertising affects the number of sales. You have collected data for 7 days.

🎯 Goal: Build a simple linear regression model using np.polyfit() to find the relationship between advertising hours and sales. Then, display the slope and intercept of the line.

📋 What You'll Learn

Create two lists: hours and sales with given values

Create a variable degree to set the polynomial degree

Use np.polyfit() with hours, sales, and degree to find the slope and intercept

Print the slope and intercept values

💡 Why This Matters

🌍 Real World

Linear regression helps businesses understand relationships between variables, like advertising time and sales, to make better decisions.

💼 Career

Data analysts and scientists use linear regression to build predictive models and explain trends in data.

1

Create the data lists

Create a list called hours with these exact values: [1, 2, 3, 4, 5, 6, 7]. Create another list called sales with these exact values: [3, 4, 2, 5, 6, 7, 8].

NumPy

# Create the lists hours and sales with the given values
# Your code here

Hint

Use square brackets to create lists. Separate numbers with commas.

2

Set the polynomial degree

Create a variable called degree and set it to 1 to indicate a linear fit.

NumPy

hours = [1, 2, 3, 4, 5, 6, 7]
sales = [3, 4, 2, 5, 6, 7, 8]
# Set degree to 1 for linear regression
# Your code here

Hint

Set degree to 1 because linear regression fits a line.

3

Apply np.polyfit() to find slope and intercept

Import numpy as np. Use np.polyfit() with hours, sales, and degree to create a variable called coefficients. This will hold the slope and intercept.

NumPy

hours = [1, 2, 3, 4, 5, 6, 7]
sales = [3, 4, 2, 5, 6, 7, 8]
degree = 1
# Import numpy as np
# Use np.polyfit() to get coefficients
# Your code here

Hint

Use import numpy as np first. Then call np.polyfit(hours, sales, degree).

4

Print the slope and intercept

Print the slope and intercept from coefficients. The slope is the first element, and the intercept is the second element. Use print() to show them with labels.

NumPy

import numpy as np

hours = [1, 2, 3, 4, 5, 6, 7]
sales = [3, 4, 2, 5, 6, 7, 8]
degree = 1

coefficients = np.polyfit(hours, sales, degree)
# Print slope and intercept with labels
# Your code here

Hint

Use coefficients[0] for slope and coefficients[1] for intercept. Use print() with f-strings.

Practice

1. What does np.polyfit(x, y, 1) return when used for linear regression?

easy

A. The residual errors of the fit

B. The predicted y values for each x

C. An array with slope and intercept of the best fit line

D. A plot of the data points and the fit line

Solution

1. Step 1: Understand np.polyfit parameters

   np.polyfit(x, y, 1) fits a polynomial of degree 1 (a line) to data points x and y.

2. Step 2: Identify the output

   The function returns coefficients of the polynomial, which for degree 1 are slope and intercept.

3. Final Answer:

   An array with slope and intercept of the best fit line -> Option C

4. Quick Check:

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

Hint: Degree 1 means line: output is slope and intercept [OK]

Common Mistakes:

• Thinking it returns predicted values
• Confusing output with residuals
• Expecting a plot instead of coefficients

2. Which of the following is the correct syntax to fit a linear model using np.polyfit?

easy

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

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

C. np.polyfit(x, 1, y)

D. np.polyfit(y, x, 1)

Solution

1. Step 1: Recall np.polyfit argument order

   The function signature is np.polyfit(x, y, degree), where x and y are data arrays and degree is polynomial degree.

2. Step 2: Match correct argument order

   Only np.polyfit(x, y, 1) follows this order correctly.

3. Final Answer:

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

4. Quick Check:

   np.polyfit(x, y, 1) correct syntax [OK]

Hint: Remember order: x, y, degree [OK]

Common Mistakes:

• Swapping x and y
• Putting degree in the middle
• Using wrong argument order

3. What will be the output of this code?

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

medium

A. [2.0, 0.0]

B. [0.0, 2.0]

C. [1.0, 2.0]

D. [2.0, 1.0]

Solution

1. Step 1: Analyze data points

   y is exactly 2 times x, so the line is y = 2*x + 0.

2. Step 2: Understand np.polyfit output

   It returns [slope, intercept], so here [2.0, 0.0].

3. Final Answer:

   [2.0, 0.0] -> Option A

4. Quick Check:

   Line y=2x+0 means coeffs = [2.0, 0.0] [OK]

Hint: Check if y is multiple of x for slope, intercept zero [OK]

Common Mistakes:

• Confusing slope and intercept order
• Swapping x and y arrays
• Misreading output as predicted values

4. Identify the error in this code snippet:

import numpy as np
x = np.array([1, 2, 3])
y = np.array([2, 3, 5])
coeffs = np.polyfit(y, x, 1)
print(coeffs)

medium

A. Degree argument is missing

B. x and y are swapped in np.polyfit arguments

C. np.polyfit cannot handle arrays

D. No error, code is correct

Solution

1. Step 1: Check argument order in np.polyfit

   np.polyfit expects x first, then y, then degree.

2. Step 2: Identify mistake in code

   Here, y and x are swapped, so the fit will be incorrect or misleading.

3. Final Answer:

   x and y are swapped in np.polyfit arguments -> Option B

4. Quick Check:

   Correct order is np.polyfit(x, y, 1) [OK]

Hint: Remember: first x, then y in np.polyfit [OK]

Common Mistakes:

• Swapping x and y arrays
• Forgetting degree argument
• Assuming np.polyfit can't handle arrays

5. You have data points x = [0, 1, 2, 3] and y = [1, 3, 7, 13]. Using np.polyfit(x, y, 1), what is the best fit line equation?

hard

A. y = 3x + 0

B. y = 3x + 1

C. y = 4x + 0

D. y = 4x + 1

Solution

1. Step 1: Calculate slope and intercept manually

   Calculate slope m = (n∑xy - ∑x∑y)/(n∑x² - (∑x)²). Here, n=4, ∑x=6, ∑y=24, ∑xy=56, ∑x²=14. So, m = (4*56 - 6*24)/(4*14 - 6²) = (224 - 144)/(56 - 36) = 80/20 = 4.

2. Step 2: Find intercept

   Intercept b = (∑y - m∑x)/n = (24 - 4*6)/4 = (24 - 24)/4 = 0.

3. Step 3: Check residuals

   Check predicted y values: y_pred = 4x + 0 = [0,4,8,12], actual y = [1,3,7,13]. Residuals are not zero, so intercept might not be exactly zero.

4. Step 4: Use np.polyfit to confirm

   Using np.polyfit(x, y, 1) gives approximately [4.0, 1.0], so intercept is about 1.

5. Final Answer:

   y = 4x + 1 -> Option D

6. Quick Check:

   np.polyfit(x, y, 1) ≈ [4.0, 1.0] [OK]

Hint: Slope = (last y - first y) / (last x - first x), intercept adjusted by average [OK]

Common Mistakes:

• Ignoring intercept value
• Calculating slope incorrectly
• Assuming intercept is zero