Linear regression basics in Data Analysis Python - Mini Project: Build & Apply

Linear regression basics

📖 Scenario: You are a data analyst at a small company. You want to understand how advertising spending affects sales. You have data for advertising spending and sales for 5 months.

🎯 Goal: Build a simple linear regression model to find the relationship between advertising spending and sales.

📋 What You'll Learn

Create a dictionary with advertising spending and sales data

Create a variable for the number of data points

Calculate the slope and intercept of the best fit line using the linear regression formula

Print the slope and intercept values

💡 Why This Matters

🌍 Real World

Linear regression is used in business to predict sales based on advertising budgets, helping companies plan their spending.

💼 Career

Data analysts and data scientists use linear regression to find relationships between variables and make predictions.

1

Create the data dictionary

Create a dictionary called data with two keys: 'advertising' and 'sales'. The value for 'advertising' should be the list [5, 10, 15, 20, 25]. The value for 'sales' should be the list [7, 12, 17, 22, 27].

Data Analysis Python

# Create the data dictionary with advertising and sales lists
# Your code here

Hint

Use a dictionary with keys 'advertising' and 'sales'. Each key should have a list of numbers as its value.

2

Set the number of data points

Create a variable called n and set it to the length of the data['advertising'] list.

Data Analysis Python

data = {'advertising': [5, 10, 15, 20, 25], 'sales': [7, 12, 17, 22, 27]}
# Create variable n for number of data points
# Your code here

Hint

Use the len() function on data['advertising'] to get the number of points.

3

Calculate slope and intercept

Calculate the slope m and intercept b of the best fit line using the formulas:
m = (n * sum(x*y) - sum(x) * sum(y)) / (n * sum(x*x) - (sum(x))**2)
b = (sum(y) - m * sum(x)) / n
Use x for data['advertising'] and y for data['sales']. Use sum() and list comprehensions to calculate sums.

Data Analysis Python

data = {'advertising': [5, 10, 15, 20, 25], 'sales': [7, 12, 17, 22, 27]}
n = len(data['advertising'])
# Calculate slope m and intercept b using linear regression formulas
# Your code here

Hint

Use zip(x, y) to multiply pairs of x and y values. Calculate sums first, then apply the formulas.

4

Print the slope and intercept

Print the slope m and intercept b values using two separate print() statements. Print "Slope:" followed by m, and "Intercept:" followed by b.

Data Analysis Python

data = {'advertising': [5, 10, 15, 20, 25], 'sales': [7, 12, 17, 22, 27]}
n = len(data['advertising'])
x = data['advertising']
y = data['sales']
sum_x = sum(x)
sum_y = sum(y)
sum_xy = sum(x_i * y_i for x_i, y_i in zip(x, y))
sum_xx = sum(x_i * x_i for x_i in x)
m = (n * sum_xy - sum_x * sum_y) / (n * sum_xx - sum_x ** 2)
b = (sum_y - m * sum_x) / n
# Print slope m and intercept b
# Your code here

Hint

Use print("Slope:", m) and print("Intercept:", b) to show the results.

Practice

1. What is the main goal of linear regression in data analysis?

easy

A. To find a straight line that best fits the data points

B. To group data points into clusters

C. To calculate the average of all data points

D. To sort data points in ascending order

Solution

1. Step 1: Understand the purpose of linear regression

   Linear regression aims to find a straight line that best represents the relationship between two variables.

2. Step 2: Compare options with the goal

   Only To find a straight line that best fits the data points describes finding a straight line that fits data points, which matches the goal of linear regression.

3. Final Answer:

   To find a straight line that best fits the data points -> Option A

4. Quick Check:

   Linear regression = best fit line [OK]

Hint: Linear regression fits a line to data points [OK]

Common Mistakes:

• Confusing regression with clustering
• Thinking regression sorts or averages data
• Mixing up regression with classification

2. Which of the following is the correct way to import the LinearRegression class from scikit-learn in Python?

easy

A. from sklearn.linear_model import LinearRegression

B. import LinearRegression from sklearn.linear_model

C. from sklearn import LinearRegression

D. import linear_model.LinearRegression

Solution

1. Step 1: Recall correct import syntax in Python

   Python uses 'from module import class' to import specific classes.

2. Step 2: Match with scikit-learn syntax

   Scikit-learn's LinearRegression is in sklearn.linear_model, so the correct import is 'from sklearn.linear_model import LinearRegression'.

3. Final Answer:

   from sklearn.linear_model import LinearRegression -> Option A

4. Quick Check:

   Correct import = from sklearn.linear_model import LinearRegression [OK]

Hint: Use 'from module import class' for specific imports [OK]

Common Mistakes:

• Using wrong import order
• Trying to import class directly from sklearn
• Using incorrect module names

3. What will be the output of this Python code using scikit-learn's LinearRegression?

from sklearn.linear_model import LinearRegression
import numpy as np

X = np.array([[1], [2], [3], [4]])
y = np.array([2, 4, 6, 8])
model = LinearRegression()
model.fit(X, y)
pred = model.predict([[5]])
print(round(pred[0], 1))

medium

A. 12.0

B. 9.0

C. 10.0

D. 8.0

Solution

1. Step 1: Understand the data and model fitting

   X values are 1 to 4, y values are 2, 4, 6, 8, which is y = 2 * x perfectly.

2. Step 2: Predict for X=5 using the fitted model

   Since y = 2 * x, prediction for 5 is 2 * 5 = 10. The code rounds to 1 decimal place, so output is 10.0.

3. Final Answer:

   10.0 -> Option C

4. Quick Check:

   Prediction = 2 * 5 = 10.0 [OK]

Hint: Check if data fits y=mx+b, then predict easily [OK]

Common Mistakes:

• Ignoring rounding in print
• Confusing input shape for predict
• Assuming wrong slope or intercept

4. Identify the error in this code snippet for fitting a linear regression model:

from sklearn.linear_model import LinearRegression
X = [1, 2, 3, 4]
y = [2, 4, 6, 8]
model = LinearRegression()
model.fit(X, y)

medium

A. LinearRegression cannot be imported from sklearn.linear_model

B. y should be a 2D array, not a list

C. model.fit requires no arguments

D. X should be a 2D array, not a 1D list

Solution

1. Step 1: Check input shapes for model.fit

   LinearRegression expects X as 2D array (samples, features). Here X is 1D list, which causes error.

2. Step 2: Confirm y shape is acceptable

   y can be 1D array/list for target values, so y is fine.

3. Final Answer:

   X should be a 2D array, not a 1D list -> Option D

4. Quick Check:

   X must be 2D for fit() [OK]

Hint: X must be 2D array for sklearn fit() [OK]

Common Mistakes:

• Passing 1D X array causes shape error
• Thinking y must be 2D
• Misunderstanding import statements

5. You have data of house sizes (in square meters) and their prices (in thousands). You want to predict the price of a house with 120 square meters using linear regression. Given these data points:

sizes = [50, 80, 100, 150]
prices = [150, 200, 250, 350]

Which code snippet correctly fits the model and predicts the price for 120 square meters?

hard

A. from sklearn.linear_model import LinearRegression
X = sizes
y = prices
model = LinearRegression()
model.fit(X, y)
pred = model.predict([120])
print(pred)

B. from sklearn.linear_model import LinearRegression
import numpy as np
X = np.array(sizes).reshape(-1,1)
y = np.array(prices)
model = LinearRegression()
model.fit(X, y)
pred = model.predict([[120]])
print(round(pred[0], 2))

C. import LinearRegression
X = sizes
model = LinearRegression()
model.fit(X, prices)
pred = model.predict(120)
print(pred)

D. from sklearn.linear_model import LinearRegression
import numpy as np
X = np.array(sizes)
y = np.array(prices)
model = LinearRegression()
model.fit(X, y)
pred = model.predict(np.array([120]))
print(pred)

Solution

1. Step 1: Prepare data in correct shape for fitting

   LinearRegression requires X as 2D array, so sizes must be reshaped with .reshape(-1,1).

2. Step 2: Fit model and predict correctly

   from sklearn.linear_model import LinearRegression import numpy as np X = np.array(sizes).reshape(-1,1) y = np.array(prices) model = LinearRegression() model.fit(X, y) pred = model.predict([[120]]) print(round(pred[0], 2)) reshapes X, fits model, predicts with [[120]] (2D), and rounds output, which is correct usage.

3. Final Answer:

   from sklearn.linear_model import LinearRegression import numpy as np X = np.array(sizes).reshape(-1,1) y = np.array(prices) model = LinearRegression() model.fit(X, y) pred = model.predict([[120]]) print(round(pred[0], 2)) -> Option B

4. Quick Check:

   Reshape X and predict with 2D input [OK]

Hint: Always reshape X to 2D before fitting and predicting [OK]

Common Mistakes:

• Not reshaping X to 2D array
• Passing 1D array to predict
• Incorrect import or usage of LinearRegression