Linear regression basics in Data Analysis Python - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the output of this linear regression coefficient calculation?

Given the following code that fits a simple linear regression model, what is the value of the coefficient for x?

Data Analysis Python

import numpy as np
from sklearn.linear_model import LinearRegression

x = np.array([[1], [2], [3], [4], [5]])
y = np.array([2, 4, 6, 8, 10])
model = LinearRegression().fit(x, y)
coef = model.coef_[0]
print(round(coef, 2))

A 10.0

B 1.0

C 0.5

D 2.0

💡 Hint

Think about the relationship between x and y in the data.

The y values are exactly twice the x values, so the slope (coefficient) is 2.0.

❓ data_output

intermediate

What is the predicted value for x=6 using this linear regression model?

Using the model trained on the data below, what is the predicted y value when x=6?

Data Analysis Python

import numpy as np
from sklearn.linear_model import LinearRegression

x = np.array([[1], [2], [3], [4], [5]])
y = np.array([3, 5, 7, 9, 11])
model = LinearRegression().fit(x, y)
pred = model.predict([[6]])[0]
print(round(pred, 2))

A 13.0

B 12.0

C 11.0

D 15.0

💡 Hint

Look at the pattern in y values as x increases.

The model fits y = 2 * x + 1, so for x=6, y = 2*6 + 1 = 13.

🔧 Debug

advanced

Why does this linear regression code raise an error?

Examine the code below. Why does it raise an error when fitting the model?

Data Analysis Python

import numpy as np
from sklearn.linear_model import LinearRegression

x = np.array([1, 2, 3, 4, 5])
y = np.array([2, 4, 6, 8, 10])
model = LinearRegression().fit(x, y)

A x must be 2D array but is 1D, causing a ValueError

B The model cannot fit because y values are not normalized

C LinearRegression requires integer inputs, but x is float

D y must be 2D array but is 1D, causing a TypeError

💡 Hint

Check the shape of x expected by scikit-learn.

scikit-learn expects x to be 2D (samples, features). Here x is 1D, so it raises ValueError.

🧠 Conceptual

advanced

Which statement best describes the intercept in linear regression?

In a simple linear regression model, what does the intercept represent?

A The maximum value y can take in the model

B The predicted value of y when x is zero

C The slope of the line showing change in y per unit x

D The error term in the regression equation

💡 Hint

Think about the point where the line crosses the y-axis.

The intercept is the value of y when x equals zero, the starting point of the line.

🚀 Application

expert

Which option correctly calculates the R-squared score for this model?

Given a fitted linear regression model and test data, which code snippet correctly computes the R-squared score?

Data Analysis Python

import numpy as np
from sklearn.linear_model import LinearRegression
from sklearn.metrics import r2_score

x_train = np.array([[1], [2], [3], [4], [5]])
y_train = np.array([2, 4, 6, 8, 10])
model = LinearRegression().fit(x_train, y_train)

x_test = np.array([[6], [7]])
y_test = np.array([12, 14])

A

r2 = model.score(y_test, x_test)
print(round(r2, 2))

B

pred = model.predict(y_test)
r2 = r2_score(x_test, pred)
print(round(r2, 2))

C

pred = model.predict(x_test)
r2 = r2_score(y_test, pred)
print(round(r2, 2))

D

r2 = r2_score(model.predict(x_test), y_test)
print(round(r2, 2))

💡 Hint

Remember the order of arguments for r2_score is (true values, predicted values).

Option C correctly predicts y_test from x_test, then computes r2_score(y_test, predictions).