Linear Regression Questions

Diwakar Bhardwaj

Score: 🔥 51

Beginner

Took 2 months

Data Science

Linear Regression

80%

Questions Attempted

15 / 15

Correct Answers

Incorrect Answers

Points Earned

🔥 12

Question 1

Which method in pandas is used to read a CSV file containing the dataset for Linear Regression?

read_csv()
loadtxt()
load()
from_csv()

Explanation:

The read_csv() function in pandas is the standard way to import data from a CSV file into a pandas DataFrame, suitable for use in Linear Regression.

Question 2

If the coefficient of determination (R-squared) for a linear regression model is 0.8, what does this indicate?

80% of the variation in the dependent variable is explained by the independent variable.
20% of the variation in the dependent variable is explained by the independent variable.
There is a weak relationship between the independent and dependent variables.
The model is a poor fit for the data.

Explanation:

R-squared, ranging from 0 to 1, represents the proportion of variance in the dependent variable that is predictable from the independent variable(s). An R-squared of 0.8 indicates a good fit, with 80% of the variation explained.

Question 3

What is the purpose of the coefficient of determination (R-squared) in linear regression?

To determine the statistical significance of the model.
To measure the proportion of variation in the dependent variable explained by the independent variable(s).
To identify the presence of outliers in the data.
To assess the linearity assumption of the model.

Explanation:

R-squared quantifies the goodness of fit of the model, indicating how well the independent variable(s) explain the variation in the dependent variable.

Question 4

What is a potential drawback of using a purely automated feature selection technique (like forward selection or backward elimination) without careful consideration?

It can lead to models that are less accurate than using all available features.
It can sometimes overlook features that might be important in combination with others.
It guarantees the most interpretable model.
It completely eliminates the need for domain expertise in model building.

Explanation:

Automated techniques may miss interactions between features. A feature unimportant on its own could be highly relevant when combined with others.

Question 5

What does the 'fit_intercept' parameter in 'LinearRegression()' control?

Whether to calculate the slope of the line.
Whether to calculate the intercept (bias) of the line.
Whether to normalize the data before fitting.
Whether to use gradient descent for optimization.

Explanation:

The 'fit_intercept' parameter in 'LinearRegression()' determines whether the model should fit an intercept term to the linear equation.

Question 6

What graphical tool is commonly used to visualize the relationship between two continuous variables in linear regression?

Histogram
Bar chart
Scatter plot
Pie chart

Explanation:

Scatter plots are the go-to visualization for exploring the relationship between two continuous variables, helping us assess linearity, direction, and strength of the association.

Question 7

Backward elimination in linear regression involves removing features based on what criterion?

The feature with the highest correlation with the target variable
The feature that results in the smallest decrease in model performance
The feature with the lowest p-value
The feature that contributes the least to multicollinearity

Explanation:

In backward elimination, features are removed one by one, selecting the feature at each step that, when removed, causes the least degradation to the model's performance.

Question 8

Who is credited as a pioneer in developing the method of least squares, a foundational element of linear regression?

Alan Turing
Ada Lovelace
Carl Friedrich Gauss
Blaise Pascal

Explanation:

Carl Friedrich Gauss, a prominent mathematician, is widely recognized for his contributions to the development of the least squares method, a fundamental technique employed in linear regression to estimate the best-fitting line through a set of data points.

Question 9

What does a residual represent in linear regression?

The predicted value of the dependent variable.
The difference between the actual and predicted values of the dependent variable.
The slope of the regression line.
The intercept of the regression line.

Explanation:

Residuals measure the vertical distance between each data point and the regression line. A positive residual means the model underpredicted, while a negative residual means it overpredicted.

Question 10

Which of these is a common visual tool for diagnosing heteroscedasticity?

Histogram
Scatter plot of residuals vs. predicted values
Box plot
Normal probability plot

Explanation:

A scatter plot of residuals against predicted values is a standard diagnostic tool for checking homoscedasticity. If the spread of residuals is relatively constant across the range of predicted values, it suggests homoscedasticity. A funnel-shaped pattern often indicates heteroscedasticity.

Question 11

Which assumption of linear regression ensures that the relationship between the independent and dependent variables is linear?

Linearity
Independence
Homoscedasticity
Normality of errors

Explanation:

Linearity is the fundamental assumption of linear regression. It assumes that the relationship between the independent and dependent variables can be best represented by a straight line.

Question 12

Which of the following is NOT a benefit of feature selection in linear regression?

Improved model interpretability
Reduced computational cost
Increased risk of overfitting
Potential for better generalization to new data

Explanation:

Feature selection actually helps to reduce the risk of overfitting. By removing irrelevant features, we prevent the model from learning noise and fitting too closely to the training data.

Question 13

A positive coefficient of the independent variable in a simple linear regression model indicates what?

As the independent variable increases, the dependent variable tends to decrease.
As the independent variable increases, the dependent variable tends to increase.
There is no relationship between the independent and dependent variables.
The independent variable has no impact on the dependent variable.

Explanation:

A positive coefficient signifies a positive linear relationship. As the independent variable increases, the dependent variable also tends to increase.

Question 14

What type of visualization tool is commonly used to initially assess the relationship between two continuous variables in linear regression?

Bar chart
Pie chart
Histogram
Scatter plot

Explanation:

Scatter plots are ideal for visualizing the relationship between two continuous variables, giving a visual indication of whether a linear relationship exists.

Question 15

Which of the following indicates a strong positive correlation between two variables?

Correlation coefficient (r) close to 0
Correlation coefficient (r) close to -1
Correlation coefficient (r) close to 1
A p-value greater than 0.05

Explanation:

A correlation coefficient close to 1 signifies a strong positive linear relationship, where both variables increase together.