Feature selection in linear regression primarily aims to:
Ensure that all features have a statistically significant p-value
Increase the number of features used for prediction
Improve model performance and generalization by focusing on the most relevant predictors
Make the model more complex and harder to interpret
How does the Mean Squared Error (MSE) penalize larger errors compared to smaller errors?
It doesn't; all errors are penalized equally.
It squares the errors, giving more weight to larger deviations.
It uses a logarithmic scale to compress larger errors.
It takes the absolute value of the errors, ignoring the sign.
Who is credited as a pioneer in developing the method of least squares, a foundational element of linear regression?
Blaise Pascal
Carl Friedrich Gauss
Ada Lovelace
Alan Turing
Why is normality of errors an important assumption in linear regression?
It ensures the linearity of the relationship between variables
It validates the use of hypothesis testing for the model's coefficients
It is necessary for the calculation of the regression coefficients
It guarantees the homoscedasticity of the errors
Which matplotlib function is commonly used to plot the regression line along with the scatter plot of the data?
hist()
plot()
show()
scatter()
What is the primary goal of feature selection in linear regression?
Improve the model's interpretability and reduce overfitting
Maximize the number of features used in the model
Increase the complexity of the model
Introduce bias into the model
If a Durbin-Watson test statistic is close to 2, what does it suggest about the residuals?
They are homoscedastic
They are independent
They exhibit a linear pattern
They are normally distributed
What distinguishes simple linear regression from multiple linear regression?
There is no difference; the terms are interchangeable.
Simple linear regression has one independent variable, while multiple linear regression has two or more.
Simple linear regression analyzes categorical data, while multiple linear regression analyzes numerical data.
Simple linear regression uses a curved line, while multiple linear regression uses a straight line.
What is the main difference between forward selection and backward elimination in linear regression?
Forward selection is used for classification, while backward elimination is used for regression.
Forward selection starts with all features and removes one by one, while backward elimination starts with no features and adds one by one.
There is no difference; both techniques achieve the same outcome.
Forward selection starts with no features and adds one by one, while backward elimination starts with all features and removes one by one.
What graphical tool is commonly used to visualize the relationship between two continuous variables in linear regression?
Scatter plot
Bar chart
Histogram
Pie chart